Statistics Syllabus for B.Sc. - Mount Carmel College, Bangalore

Statistics Syllabus for B.Sc. Mount Carmel College, Autonomous

2018 onwards

1

MOUNT CARMEL COLLEGE, AUTONOMOUS, BENGALURU

DEPARTMENT OF STATISTICS & ANALYTICS

REGULATIONS AND SYLLABUS IN STATISTICS FOR THE THREE YEAR B.Sc.

DEGREE (CBCS) COURSE

(2018 onwards)

OBJECTIVES OF THE COURSE

To impart education in Statistics, to give an in-depth knowledge of Statistics and applied topics

like time series, demography, etc. It is said that, “Knowledge of Statistics………… may prove to

be of use at any time under any circumstance”. Be it Medicine, Psychology, Astronomy,

Industry, Finance, Management or any other field, Statistics plays a very important role to make

inferences about sampled populations, to inculcate logical reasoning in students and improve

their analytical skills. In the present era of Data Science and Analytics a good grounding in

Statistics is a much desired pre-requisite.

OPPORTUNITIES

Statistics with Mathematics and Economics combination is an excellent course for students

taking up CAT exam, career in management. Software giants like Infosys, Wipro prefer

Computer Science students with a background in Statistics. The field of Actuaries requires

youngsters with a good background in Statistics. Those who desire to serve their country can

take up UPSC‟s a) Indian Statistical Service examination, b) Statistical officer in National

Sample Survey Organisation.

Clinical trials are conducted by the medical fraternity to find new and effective treatment for

diseases. The knowledge of Statistics has a vital role to play in designing the trial and in

answering medical questions effectively. A thorough grounding in Statistics is necessary for a

career in any experimental science. When numerical data regarding any biological topic is

collected, interpretation of the data can be done only with the help of Statistics. Statistics is used

to process complex problems in the real world so that Data Scientists and Analysts can look for

meaningful trends and changes in Data.

ELIGIBILITY

1. Candidate seeking admission should have passed the Pre-University or an equivalent course

with Basic Mathematics / Business Mathematics / Applied Mathematics as one of the optional

subjects.

2. Candidates taking Statistics as one of the subjects in the B. Sc. course should study

Mathematics as another optional subject.


2018 onwards

2

COMBINATIONS OFFERED

a) CMS – Computer Science, Mathematics, Statistics

b) EMS – Economics, Mathematics, Statistics

SCHEME OF INSTRUCTIONS FOR THEORY AND PRACTICAL

Bird’s Eye View of the B.Sc. Syllabus (CBCS) for Theory and Practical (2018 onwards)

Semester Title of the Paper No. of hours / week Theory Practical

TOTAL Theory Practical CIA End

Semester

CIA End

Semester

I

ST1 : Descriptive

Statistics and

Probability

04

02

30

70

15

35

150

II

ST2 : Discrete

Distributions

and Applied

Statistics

04

02

30

70

15

35

150

III

ST3 : Continuous

Distributions

04

02

30

70

15

\35

150

IV ST4 : Statistical

Inference

04

02

30

70

15

35

150

V

ST5 : Sampling

Theory and Tests

of Significance

ST6 : Design of

Experiments and

Nonparametric

Tests

03

03

03

03

30

30

70

70

15

15

35

35

150

150

VI

ST7 : Industrial

Statistics

ST8 : Operations

Research

03

03

03

03

30

30

70

70

15

15

35

35

150

150


2018 onwards

3

SCHEME OF INSTRUCTION

The Semesters I, II, III and IV have four theory or lecture hours and practical for a

duration of two hours per week.

The Semesters V and VI have six theory or lecture hours and practical for duration of three

hours per week per paper.

For the practical sessions the class shall be divided into batches for giving instructions,

supervising and correcting records. The student-teacher ratio in the batches is as per the

guidelines given by the Department of Collegiate Education, Karnataka.

In computer based practical students are required to run the programs in computers and

relevant computer outputs are to be enclosed in the practical records.

NOTE

CIA – Continuous Internal Assessment.

List of practical assignments is given under each paper in the syllabus.

The theory question papers should cover all the topics in the syllabus with proportional

weightage to the number of hours of instruction allotted.

It is expected that each student collects and uses real life data for the practical classes.

In practical examinations a maximum of 5 marks are allotted for practical records.

Additional elective papers for 6th

semester may be included in the due course.

PROGRAM OUTCOMES

The course provides a foundation and motivation for exposure to statistical ideas. The

students will be able to

Acquire the ability to bring together and flexibly apply knowledge to characterise,

analyse and solve a wide range of problems.

Recognize and appreciate the connections between theory and applications.

Independently read statistical literature of various types, including survey articles,

scholarly books and online sources.

Have the versatility to work effectively in a broad range of analytic, scientific,

government, financial, health, technical and other positions.

Choose appropriate statistical methods and demonstrate their ability to apply various

concepts in exploratory data analysis.

Use different statistical software to carry out data analysis.

Have the intellectual curiosity and flexibility to grow with developing technology and

new methods.


2018 onwards

4

SEMESTER I

THEORY PAPER I

ST1: DESCRIPTIVE STATISTICS AND PROBABILITY

Learning Outcomes

Introductory Concepts

Students will be able to

recognise different types of data and scales of measurement.

represent the data using graphs and diagrams.

Univariate Data Analysis


compute and interpret measures of centre and spread of data.

construct and analyze graphical displays to summarised data.

Bivariate Data Analysis


calculate, interpret and communicate the simple correlation and simple linear regression.

fit different types of curves to the respective data.

Probability


utilize basic concepts of probability including independence and conditional probability.

calculate, interpret and communicate event probabilities.

evaluate probabilities of events from two-way tables.

Module I (8 hours)

Introductory Concepts

Unit 1

Introduction to the subject of Statistics, population and sample, variables and attributes.

Unit 2

Types of data – qualitative, quantitative, univariate, multivariate, cross sectional, time series,

discrete, continuous, primary, secondary. Scales of measurement – nominal, ordinal, interval,

ratio.

Unit 3

Construction of frequency distributions (univariate and bivariate).

Organisation and presentation of data through diagrams (bar and pie) and graphs (frequency

curve, histogram, cumulative frequency curves), stem and leaf plot.


2018 onwards

5

Module II (18 hours)

Univariate Data Analysis

Unit 1

Measures of location or central tendency - arithmetic mean, median, mode, geometric mean,

harmonic mean – properties, positional averages or quantiles – quartiles, deciles, percentiles and

their interpretations. Comparison of the different averages.

Unit 2

Measures of dispersion - absolute measures - range, mean deviation, quartile deviation, standard

deviation - properties with proof, relative measures.

Unit 3

Moments – about origin, about an arbitrary point, central moments, relationship between

moments about origin and moments about mean, skewness and kurtosis - concept and measures,

box and whisker plot – construction and applications.

Module III (10 hours)

Bivariate Data Analysis

Unit 1

Linear Correlation - Scatter diagram, product moment correlation coefficient - properties,

Spearman‟s rank correlation coefficient.

Unit 2

Regression - Dependent and independent variables, objectives of regression, derivation of linear

regression model by the method of least squares, estimation of regression coefficient and

coefficient of determination and their interpretations.

Module IV (16hours)

Probability

Unit 1

Introduction to probability, sample space and events, various approaches to probability –

classical, empirical and axiomatic approach

Unit 2

Addition theorem, conditional probability, multiplication theorem, independent events,

Theorems related to the different concepts, Bayes‟ theorem, rule of total probability.


2018 onwards

6

PRACTICAL – STP1

1. Data Presentation

2. Measures of Central Tendency

3. Measures of Dispersion, Skewness, Kurtosis

4. Correlation and Regression for Ungrouped Data

5. Probability 1

6. Probability 2

BOOKS FOR STUDY

1. Medhi J - Statistical Methods - An Introductory Text, Second Edition, New Age

Publishers (2006)

2. Goon A M, Gupta M K and Das Gupta B - Fundamentals of Statistics - Volume I, Sixth

Edition, World Press, Calcutta (1986)

3. Gupta S C and Kapoor V K - Fundamentals of Mathematical Statistics, Sultan Chand and

Sons (2017)

4. Kapoor J N and Saxena H C - Mathematical Statistics, Sultan Chand and Company (2014)

5. Roger E Kirk - Statistics: An Introduction, Fifth Edition, Wadsworth Publishing Company

(2007)

6. Bhat B R, Srivenkataramana T and Rao Madhava K. – Statistics : A Beginner's Text,

Volume I and II, New Age International Pvt Ltd (1996)

7. Mukhopadhyay P - Mathematical Statistics, New Central Book Agency (1996)

BOOKS FOR REFERENCE

1. Agarwal B L - Basic Statistics, Sixth Edition, New Age International Pvt Ltd (2013)

2. Stirzaker, David - Elementary Probability, Second Edition, Cambridge University Press

(2003)

3. Snedecor G W and Cochran - Statistical Methods, Eighth Edition, Affiliated East West Press

Ltd (1989)

4. Sheldon M Ross - Introductory Statistics, Second Edition, Academic Press(2010)

5. Freund J E and Walpole - Mathematical Statistics, New Edition, Prentice Hall India (2012)


2018 onwards

7

SEMESTER II

THEORY PAPER II

ST2: DISCRETE DISTRIBUTIONS AND APPLIED STATISTICS

Learning Outcomes

Discrete Random Variables and Theoretical Discrete Probability Distributions


construct probability distribution of a discrete random variable.

determine the appropriate theoretical probability distribution based on experimental

conditions and assumptions.

calculate, interpret and communicate probabilities.

Applied Statistics

Index Numbers


understand and identify the problems in the construction of various types of index numbers.

appreciate various tests of adequacy and the uses of index numbers.

understand the concept of Consumer Price Index and identify the limitations of index

numbers.

Time Series


understand and apply the concepts and methods underlying the analysis of univariate time

series and the context for interpretation of results.

decompose a time series into trend, seasonal, cyclical and irregular components.

understand the theoretical basis of different methods of time series analysis including

decomposition.

Official Statistics

Students will know

about the Ministry of Statistics and Programme Implementation (MoSPI).

about the functions of NSSO and CSO.

Demography

The students will be able to

Understand basic demographic measures.

Identify alternative sources of demographic data.

Analyse and interpret basic demographic measures.


2018 onwards

8

Demand Analysis

The students will be able to

define and explain the utility analysis.

define supply and demand analysis and explain the associated functions.

explain how supply and demand are related.

Module I (12 hours)

Discrete Random Variables

Unit 1

Concept of a random variable, distribution function and its properties, discrete random variable

and its probability function, mathematical expectation of a random variable - mean, variance and

higher moments. Properties of expectation and variance.

Unit 2

Bivariate probability distribution, marginal and conditional distributions, covariance,

independence, conditional expectation and variance, mean and variance of linear combination of

random variables.

Unit 3

Moment generating function (mgf) and its properties, methods of generating moments from mgf.


Theoretical Discrete Distributions

Unit 1

Uniform distribution- mean and variance.

Unit 2

Bernoulli distribution- probability mass function (pmf), mean, variance, moment generating

function.

Binomial distribution- derivation of the pmf, mean, variance, moments, moment generating

function, recurrence relation for moments and probabilities, coefficients of skewness and

kurtosis, additive property, fitting.

Poisson distribution- derivation of pmf, mean, variance, moments, moment generating function,

recurrence relation for moments and probabilities, additive property, fitting.

Unit 3

Hyper-geometric distribution- mean, variance, limiting form.

Unit 4

Geometric distribution- mean, variance, moments, moment generating function, additive

property, lack of memory property.

Negative binomial distribution – mean, variance, moments, moment generating function,

recurrence relation for moments.


2018 onwards

9


Applied Statistics - I

Unit 1

Index Numbers

Meaning, uses, problems in the construction of index numbers, price and quantity relatives,

simple aggregative and weighted price and quantity index numbers, Laspeyre, Paasche,

Marshall - Edgeworth and Fisher index numbers – their inter-relationships, tests for index

numbers, consumer price index number and methods of constructing them.

Unit 2

Time Series

Components of time series, additive and multiplicative models, measurement of trend – method

of semi averages, method of least squares and method of moving averages, measurement of

seasonal variation- method of simple averages, method of ratio to moving averages; applications

of time series.

Module IV (15 hours)

Applied Statistics - II

Unit 1

Official Statistics

Ministry of Statistics and Programme Implementation (MoSPI), Chief Statistician of India,

indices of economic growth, functions of NSSO and CSO and their principle findings, national

income, per capita income, gross domestic product.

Unit 2

Demography

Sources of demographic data, measures of morbidity and mortality - crude, specific and

standardised death rates, maternal mortality rate, infant mortality rate, measurement of fertility-

crude, age-specific, general and total fertility rates, reproductive rates - gross and net, life tables

– cohort, components, construction, uses.

Unit 3

Demand Analysis

Law of demand and supply, elasticity of demand and supply, Giffen‟s paradox, Utility function,

marginal utility function, statement of law of diminishing marginal utility, statement of law of

equi-marginal utility.


2018 onwards

10

PRACTICAL – STP2

1. Computation of Characteristics for Discrete Probability Distributions

2. Computation of Characteristics for Bivariate Probability Distributions

3. Evaluation of Probabilities involving Discrete Theoretical Distributions

4. Fitting of Binomial, Poisson and Negative Binomial Distributions

5. Time Series

6. Construction of Index Numbers

7. Demography

8. Data Analysis using Statistical Software ( MSEXCEL, SPSS )

a) Diagrams and Graphs

b) Measures of Central Tendency and Dispersion

c) Correlation and Regression for Ungrouped Data

BOOKS FOR STUDY

1. Irwin Miller, Marylees Miller - John E Freund‟s Mathematical Statistics, Eighth Edition,

Prentice Hall India (2012)

2. Harry Frank and Steven C Althoen, Statistics - Concepts and Application, Cambridge

Low Price Edition (1994)

3. Gupta. S C and Kapoor V K - Applied Statistics, Sultan Chand and Sons (2014)

4. Sheldon M Ross - Introductory Statistics, Second Edition, Academic Press (2010)

5. Hogg R V, Tanis E A - Probability and Statistical Inference, Eighth Edition (2010)

6. Goon A M, Gupta M K and Dasgupta B - Fundamentals of Statistics - Volume II,

World Press (2016)

7. Bhuyan K C - Probability Distribution Theory and Statistical Inference, NCBA(2010)

BOOKS FOR REFERENCE

1. Neil A Weiss - Elementary Statistics, Ninth Edition, Addison Wesley (2016)

2. Spiegel M R and Stephens L J - Theory and Problems of Statistics, Third Edition,

Schaum‟s Publishing Company (1999)

3. Richard A Johnson - Miller & Freund‟s Probability and Statistics for Engineers,

Eighth Edition, Prentice Hall (2011)

4. Parimal Mukhopadyay - Applied Statistics, Books and Allied Pvt Ltd (1999)

5. Peter Dalgaard - Introductory Statistics for R, Second Edition, Springer (2013)


2018 onwards

11

SEMESTER III

THEORY PAPER III

ST3: CONTINUOUS DISTRIBUTIONS

Learning Outcomes

Continuous Random Variables


understand different probability functions with respect to univariate and bivariate continuous

random variables.

prove the properties and theorems on expectation and variance.

derive the distribution of functions of univariate random variables using appropriate

techniques.

Theoretical Continuous Distributions


determine the appropriate areas under a normal curve.

prove important properties of normal distribution including the preservation of normality

under a linear transformation.

derive the properties of other theoretical continuous distributions like uniform, exponential,

beta and gamma.

Sampling Distributions


describe the abstract idea of a sampling distribution and how it reflects the sample to sample

variability of a statistic.

explain how it is a measure of the precision of a point estimate (sampling variability).

know about chi-square, t and F distributions – their genesis and properties.

Limit Theorems


apply the central limit theorem to problems involving sums and averages of variables from

arbitrary distributions.

understand the applications of Chebychev‟s inequality.


2018 onwards

12

Module I (13 hrs)

Continuous Random Variables

Unit 1

Concept of a random variable, continuous random variable and its probability density function,

distribution function and its properties.

Unit 2

Expectation of a random variable - mean, variance skewness and kurtosis, transformation of

univariate random variables using cdf and transformation techniques.

Unit 3

Bivariate probability distribution, marginal and conditional distributions, independent random

variables, conditional expectation, conditional variance and proof of the associated theorems,

covariance, correlation, moment generating function.

Module II (18 hrs)

Theoretical Continuous Distributions

Unit 1

Uniform, beta (type 1 and type 2), exponential and gamma distributions – definition through

probability density function, mean, variance, moments and moment generating function, additive

property of exponential and gamma variates, lack of memory property of exponential

distribution. Normal distribution and its properties –median, mode, m.g.f, moments, area and

additive property, points of inflexion. Cauchy distribution- definition, statement of properties.

Unit 2

Bivariate normal distribution- definition through p.d.f, marginal and conditional distributions.

Module III (16 hrs)

Sampling Distributions

Unit 1

Concepts of population, parameter, random sample, statistic, sampling distribution and standard

error, sampling distributions of sample mean, biased and unbiased estimators of population

variance, statement of theorem on independence of sample mean and variance in random

sampling from normal distribution, sampling distribution of sample variance.

Unit 2

Chi-square, t and F distributions - definition through probability density function and important

properties.


2018 onwards

13

Module IV (05 hrs)

Limit Theorems

Unit 1

Chebychev‟s inequality – proof with respect to continuous random variable, applications.

Unit 2

Convergence in probability and convergence in distribution

Central limit theorem – Statement in its general form and applications, proof of De'Moivre -

Laplace and Levy - Lindeberg theorems.

PRACTICAL – STP3

1. Computation of Characteristics of Continuous Probability Distribution

2. Computation of Characteristics of Bivariate Probability Distribution

3. Transformation of Univariate Random Variables

4. Evaluation of Probabilities of Normal Distribution

5. Evaluation of Probabilities of Exponential, Uniform, Beta and Gamma distributions

6. Fitting of Normal Distribution

7. Construction of Sampling Distribution of Sample Mean and Sample Variance

8. Applications of Chebychev‟s Inequality and Central Limit Theorem

9. Computer aided Data Analysis (MSEXCEL, SPSS)

a) Correlation and Regression (for 2018 and 2019 batches only)

b) Evaluation of Probabilities of Theoretical Discrete and Continuous Distributions

(from 2019 batch onwards)

BOOKS FOR STUDY

1. Sharma A K - Text Book of Probability and theoretical Distributions, Discovery Publishing

House, New Delhi (2005)

2. Hogg, Tanis, Rao - Probability and Statistical Inference - Seventh Edition, Pearson Education

(2011)

3. Bhuyan K C – Probability, Distribution Theory and Statistical Inference , NCBA (2010)

4. Ball Alan, Buckwell Geoff - A Level Statistics, Macmillan Work out Series (2016)

5. Miller Irwin, Miller Marylees - John E Freund‟s Mathematical Statistics and Applications,

Eighth Edition, Pearson (2018)

6. Gupta S C, Kapoor V K - Fundamentals of Mathematical Statistics, Sultan Chand & Sons

(2017)

7. Goon A M , Gupta M K , Das Gupta B - Fundamentals of Statistics, Volume I, World Press,

Calcutta(1991)

8. Hogg R V and Craig A T - Introduction to Mathematical Statistics, Fifth Edition, Prentice

Hall, New Jersey, USA (1995)


2018 onwards

14

9. Medhi J - Statistical Methods: An Introductory Text, New Age International, New Delhi

(1992)

10. Mukhopadhyay P - Mathematical Statistics, Books and Allied Pvt Ltd., Kolkata (2015)

11. Spiegel M R - Probability and Statistics, Fourth Edition, Schaum‟s Outline Series, McGraw

Hill, London (2001)

12. Walpole R E , Myers R H , and Myers, S L - Probability and Statistics for Engineers and

Scientists, Ninth Edition, Pearson, New Delhi (2017)

BOOKS FOR REFERENCE

1. Spatz Chris - Basic Statistics: Tales of Distributions, Tenth Edition, Wadsworth Cengage

Learning (2010)

2. DeCoursey W J - Statistics and Probability for Engineering Applications with Microsoft

Excel , Elsevier Science (USA) ( 2003)

3. Krishnamoorthy K - Handbook of Statistical Distributions with Applications, Chapman and

Hall/CRC (2006)

4. Beaver Barbara M, Beaver Robert J, Mendenhall William - Introduction to Probability

and Statistics, Twelfth Edition, Cengage Learning

5. Lipschutz Seymour, Schiller John J - Introduction to Probability and Statistics (Schaum‟s

Outlines), Tata McGraw Hill (2014)

6. Fricker Jr. Ronald D -Introduction to Probability and Statistics for Data Scientists(with R):

Chapters 1-3, CreateSpace Independent Publishing Platform (2014)

7. Bhattacharya G K and Johnson R A - Statistical Concepts and Methods, John Wiley, New

York (1986)

8. Dudewicz E J and Mishra S N - Modern Mathematical Statistics, John Wiley, New York

(1980)

9. Rohatgi V K and Saleh A K Md. E. - An Introduction to Probability Theory and

Mathematical Statistics, Third Edition, John Wiley, New York (2002)

10. Ross S M - Introduction to Probability Models, Tenth Edition, Academic Press, UK(2003)


2018 onwards

15

IV SEMESTER

THEORY PAPER IV

ST4: STATISTICAL INFERENCE

Learning Outcomes

Point Estimation and Methods of Estimation


appreciate the need for statistical inference and point estimation of the parameters.

compute point estimates of the parameters of theoretical discrete and continuous

distributions.

utilise the of method of maximum likelihood function and method of moments of obtaining

point estimators.

Testing of Hypothesis and Most Powerful (MP) Tests


identify the appropriate null and alternative hypotheses, including one or two sided, simple or

composite for a given study objective.

identify correctly what the type I and type II errors would be when presented with the results

of a statistical study.

apply Neyman-Pearson lemma for constructing most powerful tests.

Uniformly Most Powerful (UMP) and Likelihood Ratio (LR) Tests


identify families of distributions that possess the monotone likelihood ratio(MLR) property.

apply the MLR property in the construction of uniformly most powerful tests.

Interval Estimation


understand the informal and formal explanations of any confidence interval.

understand how factors like sample size, confidence level, estimated standard deviation of

estimator (i.e., standard error) and margin of error affect the width and precision of a

confidence interval.

distinguish between one-sided and two-sided confidence intervals.

construct intervals for common population parameters (means, proportions, variances and

population correlation coefficient).


2018 onwards

16

Module I (18 hrs)

Point Estimation and Methods of Estimation

Unit 1

Concepts of parameter, estimator, estimate and standard error of an estimator, unbiasedness,

asymptotic unbiasedness, mean squared error, bias, relationship between bias, mean squared

error and variance, consistency, statement of sufficient conditions for consistency of an

estimator, invariance property of consistent estimators, sufficient statistic, factorisation theorem,

invariance property of sufficient estimators, efficiency, relative efficiency, Fisher information

function, statement of Frechẻt - Cramer – Rao inequality, minimum variance bound (MVB)

estimator, minimum variance unbiased estimator (MVUE), difference between MVU and MVB

estimators. Identifying unbiased, consistent, efficient, sufficient and minimum variance bound

estimators of parameters of standard theoretical discrete and continuous probability distributions.

Unit 2

Maximum likelihood and moment methods of estimation, examples, statement of properties.

Module II (14 hrs)

Testing of Hypothesis and Most Powerful Tests

Unit 1

Statistical hypotheses - null and alternative, simple and composite, one and two sided; critical

and acceptance regions and critical (test) function, randomized and non-randomized tests, type-I

and type-II errors, level of significance, size and power of a test, p-value.

Unit 2

Most powerful (MP) test, statement of Neyman-Pearson lemma and its uses in the construction of

most powerful tests, applications.

Module III (10 hrs)

Uniformly Most Powerful and Likelihood Ratio Tests

Unit 1

Monotone likelihood ratio (MLR) property, uniformly most powerful (UMP) test, statement of

the theorem on uniformly most powerful tests for testing one sided hypotheses for distributions

with monotone likelihood ratio property, applications.

Unit 2

Likelihood ratio tests (LRT), likelihood ratio tests for testing the mean of univariate normal

distribution (case of simple null against a two sided alternative).


2018 onwards

17

Module IV (10 hrs)

Interval Estimation

Unit 1

Meaning, confidence coefficient, margin of error, length and precision of confidence intervals,

pivotal quantity, one and two sided confidence intervals, central and shortest confidence

intervals.

Unit 2

Confidence interval for mean, difference of means, variance, ratio of variances, proportion,

difference between proportions and correlation coefficient.

PRACTICAL – STP4

1. Estimation of Parameters by the Method of Maximum Likelihood and Method of Moments

2. Evaluation of Probabilities of Type I and Type II Errors and Power of Tests (Discrete

Distributions)

3. Evaluation of Probabilities of Type I and Type II Errors and Power of Tests

(Continuous Distributions)

4. Construction of MP test – I (Discrete Distributions)

5. Construction of MP test – II (Continuous Distributions)

6. Construction of UMP Tests and Power Curve for Exponential and Normal Distributions

7. Interval Estimation

8. Computer Aided Data Analysis (MS EXCEL, R, SPSS) – Interval Estimation

BOOKS FOR STUDY

1. Hogg, Tanis, Rao - Probability and Statistical Inference - Seventh Edition, Pearson

Education (2011)

2. Hogg, McKean and Craig - Introduction to Mathematical Statistics - Seventh Edition,

Pearson Education (2013)



4. Goon A M , Gupta M K and Das Gupta B - Outline of Statistical Theory - Vol.1, World

Press, Calcutta (1991)

5. Gupta S C, Kapoor V K - Fundamentals of Mathematical Statistics - Sultan

Chand &Sons (2017)

6. Medhi J - Statistical Methods: An Introductory Text, New Age International, New Delhi

(1992)



8. Rajagopalan M, Dhanavanthan P – Statistical Inference –PHI Learning Pvt Ltd (2012)


2018 onwards

18

BOOKS FOR REFERENCE

1. Tucker H G - An Introduction to Probability and Mathematical Statistics, Academic Press

(2014)

2. Casella G, Berger R L – Statistical Inference, Duxbury Thomson Learning (2002)

3. Panik Michae J – Statistical Inference : A short Course, Wiley (2012)

4. DeCoursey W J - Statistics and Probability for Engineering Applications with Microsoft

Excel, Elsevier Science, USA (2003)

5. Gupta Bhisham C and Guttman Irwin - Statistics and Probability with Applications for

Engineers and Scientists, Wiley (2013)

6. Wackerly Dennis D, Mendenhall William III, Scheaffer Richard L – Mathematical Statistics

with Applications, Seventh Edition, Cengage Learning (2008)

7. Mood AM, Greybill FA and Boes D C - Introduction to the Theory of Statistics – McGraw

Hill, Third Edition, Seventh Reprint (2001)

8. Rohatgi V K and Saleh A K Md E - An Introduction to Probability and Statistics, Third

Edition, Wiley (2015)

9. Bijma F, Jonker M, Vaart A – An Introduction to Mathematical Statistics, Second Edition,

Amsterdam University Press (2017)

10. Kandethody M Ramachandran, Chris P Tsokos - Mathematical Statistics with Applications

in R, Second Edition, Elsevier (2015)


2018 onwards

19

V SEMESTER

THEORY PAPER V

ST5: SAMPLING THEORY AND TESTS OF SIGNIFICANCE

Learning Outcomes

Basic Concepts and Survey Methods


identify the population of interest, individuals, parameter, sample and statistics from a study.

distinguish between (i) an observational study and an experiment. (ii) probability and non

probability sampling methods – the methodology of each of the types considered.

identify whether a probability sampling method or a non-probability sampling method was

used to obtain the study data.

distinguish between the accuracy and precision of estimates.

Simple Random Sampling, Stratified Random Sampling and Systematic Random Sampling


learn about a variety of sampling methods, namely, simple random sampling, stratified

random sampling and systematic sampling.

understand how results from samples can be used to provide estimates of population

characteristics such as population mean, population total, population standard deviation and

/or population proportion.

calculate the interval estimates of the parameters.

compare and recognize the best method of sampling.

Tests of Significance


recognise the similarity among all test statistics of the standardized score variety; exploit this

similarity to derive test statistics for common tests involving proportions and means.

use p-values to make decisions about hypotheses under test.

correctly identify the appropriate statistical test that should be applied to analyze a study,

choosing from proportion(s), mean(s), variance(s) correlation/linear regression,

independence of attributes and goodness of fit and also use statistical software for this

analysis.


2018 onwards

20

Module I (5 hours)

Basic Concepts and Survey Methods

Unit 1

Concept of finite population and sample, need for sampling – complete enumeration versus

sample surveys, non- probability and probability sampling – meaning , need and illustrations

with respect to different techniques; methods of drawing random samples – lottery system , use

of random numbers; bias, accuracy and precision of the estimates.

Unit 2

Sample design – its meaning and importance, principle steps in a survey, sampling and non –

sampling errors and simple methods of controlling them, requisites of a good questionnaire,

drafting of questionnaires and schedules, pilot survey.


Simple Random Sampling

Unit 1

Simple random sampling with and without replacement, unbiased estimators of population mean

and total, derivation of sampling variances and their estimation, confidence limits for population

mean, population total, derivation of formulae for sample size in sampling for means using

SRSWOR.

Unit 2

Simple random sampling for attributes, unbiased estimators of population proportion and total

number of units possessing the attribute in the population, derivation of their standard errors and

confidence limits for the true values; derivation of formula for sample size in sampling for

proportions.


Stratified Random Sampling and Systematic Random Sampling

Unit 1

Need for stratification, unbiased estimators of population mean and total, allocation of sample

sizes under proportional, optimum and Neyman allocations, derivation of standard errors and

their estimation under proportional and Neyman‟s allocations, proof of the theorem under

optimum allocation with a fixed sample size, comparison of Vopt , Vprop and Vsrs . Expressions for

gain in precision due to stratification over SRSWOR.

Unit 2

Linear and circular systematic sampling, advantages and limitations, estimation of population

mean and standard error of the estimator, comparison of systematic sampling with simple

random sampling, systematic sampling as a particular case of stratified random sampling.


2018 onwards

21


Tests of Significance

Unit 1

Revision of basic terms (types of hypotheses, errors, tests, critical and acceptance regions). Tests

for mean and equality of two means, tests for variance and equality of two variances, large

sample tests for proportion and equality of two proportions.

Unit 2

Tests for linear correlation coefficient and regression coefficient in simple linear regression, chi-

square tests for goodness of fit and for independence of attributes in a contingency table.

PRACTICAL – STP5

PART A

1. Design of Questionnaires. (Their pretest and subsequent modifications, if required)

2. Simple Random Sampling

3. Stratified Random Sampling

4. Systematic Random Sampling

5. Tests concerning Population Mean and Equality of Two Population Means

6. Tests concerning Population Proportion and Equality of Two Population Proportions

7. Tests concerning Population Variance and Equality of Two Population Variances

8. Tests concerning Population Correlation and Regression Coefficients

9. Chi-square Test for Goodness of Fit

10. Chi-square Test for Independence of Attributes

11. Computer Aided Data Analysis - Tests of Significance

{The numerical examples with 'sample data given' are handled using the following software:

Test for single mean, two means independent samples & paired t test - EXCEL, R and SPSS

Test for two variances – EXCEL and Test for proportions – R}

PART B

FIELD/PROJECT WORK

The students shall divide themselves into smaller groups. They shall decide on a topic of

interest, give a survey proposal , conduct pilot survey, modify questions if necessary, collect

data , analyze and write a report, using a public domain software, like „R‟.


2018 onwards

22

BOOKS FOR STUDY

1. Cochran W G - Sampling Techniques, Third Edition, Wiley Student Edition (2014)

2. Singh Daroga, Chaudhary F S - Theory and Analysis of Sample Survey Designs, First

Edition, New Age International Private Limited (2018)

3. Mukhopadhyay Parimal - Theory and Methods of Survey Sampling, Second Edition,

Prentice Hall India Learning Private Limited (2008)

4. Casella George, Berger Roger L - Statistical Inference, Second Edition, Cengage Learning

(2001)

5. Hogg R V, Tanis E A and Zimmerman D L - Probability and Statistical Inference, Ninth

Edition, Pearson Education (2015)

6. Mood A M, Graybill F A and Boes D C - Introduction to the Theory of Statistics, Third

Edition, McGraw Hill (2001)

BOOKS FOR REFERENCE

1. Raj D, Chandak P – Sample Survey Theory, Createspace Independent Publishing Platform

(2013)

2. Sampath S - Sampling Theory and Methods, Illustrated Edition, Alpha Science

International (2005)

3. Sukhatme P V et.al - Sampling Theory of Surveys with Applications, Third Revised

Edition, Iowa State University Press (1984)

4. Ross S M - Introduction to Probability and Statistics for Engineers and Scientists, Fifth

Edition, Academic Press (2014)

5. Rao C R - Linear Statistical Inference and its Applications, Second Edition, Wiley (2002)

6. Rohatgi V K and Saleh A K Md E - An Introduction to Probability and Statistics, Third

Edition, Wiley (2015)


2018 onwards

23

V SEMESTER

THEORY PAPER VI

ST6: DESIGN OF EXPERIMENTS AND NONPARAMETRIC TESTS

Learning Outcomes

Analysis of Variance (ANOVA)


recognise the situation in which analysis of variance (ANOVA) is appropriate and be able to

perform one-way and two-way ANOVA with the assistance of computer software.

explain the partitioning of the total sum of squares into the “within” and “between” group

components and identify the degrees of freedom associated with each sum of squares.

perform the F test in ANOVA, evaluating or approximating the p-value of the test statistic.

Design of Experiments


identify features common in experiments, like the experimental unit, treatment, factors,

control groups, randomisation and blocking.

understand the importance of statistical design of experiments and its benefits; to choose an

appropriate experimental design based on the study objectives.

design and conduct appropriate experiments, as well as analyse and interpret appropriate

experimental data.

understand the concept of efficiency of an experimental design.

Factorial Experiments


understand the need and the procedure of conducting factorial experiments.

analyse two factor and three factor factorial experiments at two levels.

appreciate the need for confounding a factorial experiment, identify the confounded effect.

Nonparametric Tests


compare and contrast parametric and nonparametric tests and to identify applications where

nonparametric approaches are appropriate.

explain in detail and demonstrate the conduct of some non-parametric tests (in the framework

of large sample approximation of the test statistic).


2018 onwards

24

Module I (10 hours)

Analysis of Variance (ANOVA)

Unit 1

Introduction - Meaning and assumptions, various mathematical models used in analysis of

variance.

Unit 2

Analysis of fixed effect model – one-way and two-way classified data - discussion through

examples, complete analysis, expected mean squares, least significant difference. Two way

classified data with interaction effect (only discussion with examples).


Design of Experiments

Unit 1

Introduction of basic terms: experimental material, experimental units, treatments, response,

blocks, etc., principles of randomization, replication and local control.

Unit 2

Completely Randomized Design (CRD), Randomized Block Design (RBD) and Latin Square

design (LSD) - layout and analysis, advantages, limitations and applications; efficiency of a

design, relative efficiency of RBD over CRD and LSD over CRD and RBD; missing plot

technique for RBD and LSD- estimation of single missing observation followed by analysis.


Factorial Experiments

Factorial experiments- meaning and need; 2² and 23 factorial experiments conducted as CRD and

RBD – complete statistical analysis - main effects and interactions, their estimates, contrast and

orthogonal contrasts, Yates‟ method of computing factorial effect totals; confounding in factorial

experiments - complete and partial confounding in a 23 experiment with RBD layout- analysis

and inference.


Nonparametric Tests

Need, advantages and limitations of nonparametric tests, comparison with parametric tests;

discussion of the large sample approximation, construction of the test statistic and inference with

respect to the following tests - sign, run, median, signed rank, Wilcoxon rank sum, Mann-

Whitney -Wilcoxon U, Spearman‟s rank correlation coefficient, Kolmogorov-Smirnov test for

goodness of fit .


2018 onwards

25

PRACTICAL – STP6

1. Analysis of Variance for a One Way Classified Data

2. Analysis of Variance for a Two Way Classified Data

3. Analysis of CRD, RBD and LSD

4. Analysis of a RBD and LSD with a Single Missing Observation

5. Analysis of 2² Factorial Experiment

6. Analysis of 23 Factorial Experiment

7. Analysis of a Confounded 23 Factorial Experiment

8. Computer Aided Data Analysis (SPSS, R and MSEXCEL) – ANOVA

9. Nonparametric Tests

BOOKS FOR STUDY

1. Cochran W G and Cox G M - Experimental Designs, Second Edition, John Wiley (2003)

2. Das M N and Giri N C - Design and Analysis of Experiments, Second Edition, New Age

International Pvt Ltd (2011)

3. Agarwal B L – Theory and Analysis of Experimental Designs –Cbs Publishers & Distributors

(2011)

4. Panneerselvam R - Design And Analysis Of Experiments – Prentice Hall of India (2012)

5. Montgomery D C - Applied Statistics and Probability for Engineers, Fourth Edition, Wiley

India Pvt. Ltd. (2009)

6. Conover W J - Practical Nonparametric Statistics, Third Edition, Wiley (2006)

BOOKS FOR REFERENCE

1. Montgomery D C - Design and Analysis of Experiments, Eighth Edition, John Wiley

(2012)

2. Joshi D D- Linear Estimation and Design of Experiments, New Age International (2009)

3. Walpole RE, Myers RH, Myers SL and Ye K - Probability and Statistics for Engineers and

Scientists, Ninth Edition, Pearson (2016)

4. Johnson, R A and Bhattacharya G K - Statistical Principles and Methods, Seventh Edition,

Wiley India Pvt. Ltd. (2015)

5. Dean Angela, Voss Daniel and Draguljic Daniel - Design and Analysis of Experiments,

Second Edition, Springer (2017)

6. Ross S M - Introduction to Probability and Statistics for Engineers and Scientists, Fifth

Edition, Academic Press (2014)

7. Berger P D and Maurer R E - Experimental Design with Applications in Management,

Engineering and the Sciences, First Edition, Duxbury Press (2001)

8. Zappe Christopher , Albright S C , Winston W L - Data Analysis and Decision Making

with Microsoft Excel, Brooks/Cole (2010)

9. Wackerly Dennis D, Mendenhall William III, Scheaffer Richard L – Mathematical Statistics

with Applications, Seventh Edition, Cengage Learning (2008)


2018 onwards

26

VI SEMESTER

THEORY PAPER VII

ST7: INDUSTRIAL STATISTICS

Learning Outcomes

Introduction to Statistical Quality Control (SQC)

Students will be able to understand

the aims and objectives of SQC.

the different quality tools and quality standards.

Process Control


construct control charts for variables and attributes.

interpret the results of process capability studies.

Product Control


understand the meaning of product control and the role of sampling plans.

evaluate the different characteristics of single sampling plans and interpret them.

Reliability

Students will

learn the basic reliability concepts.

be able to calculate failure rate assuming different probability distributions.

get exposed to practical applications – real life situations where these probability models are

used.

Module I (6 hours)

Introduction to Statistical Quality Control (SQC)

Aims and objectives of statistical quality control, chance and assignable causes of variation,

process control, product control, importance of statistical quality control in industry, seven

quality control tools, total quality management, quality standards - BIS, ISO and six sigma.


2018 onwards

27


Process Control

Unit 1

Theoretical basis and practical background for control charts, 3σ control limits, probability

limits, warning limits, natural tolerance and specification limits, rational subgroups.

Unit 2

Control chart for variables - derivation of limits and construction of X -R and X -s charts and

interpretation, process capability studies. OC and ARL functions of X -R charts.

Unit 3

Control chart for attributes- charts for number of defectives and fraction defective (d and p),

charts for number of defects (c and u) – basis, construction and interpretation, applications.

Model III (10 hours)

Product Control

Unit 1

Sampling inspection and 100 % inspection, acceptance sampling, Single Sampling Plan(SSP) for

attributes, AQL, LTPD, producer‟s risk and consumer‟s risk, derivation of OC, AOQ, ASN and

ATI functions for a single sampling plan, construction of a single sampling plan using Dodge -

Romig tables.

Unit 2

Double sampling plan (DSP) for attributes - description, advantages over single sampling plan,

derivation of the OC function, expressions for ASN, ATI and AOQ functions for a double

sampling plan


Reliability

Reliability concepts, reliability of components and systems, reliability function, hazard rate, life

distributions- exponential, gamma and Weibull, system reliability-series and parallel systems,

Discussion on real-life applications/examples.


2018 onwards

28

PRACTICAL – STP7

1. Construction of X -R Control Charts

2. Construction of X -s Control Charts

3. Construction of OC and ARL curves for X -R charts

4. Construction of d and p Control Charts

5. Construction of c and u Control Charts

6. Single Sampling Plan – Characteristics and Construction

7. Reliability

8. Computer Aided Data Analysis - Construction of Control Charts (SPSS, R)

BOOKS FOR STUDY

1. Grant E L and Leavenworth R S - Statistical Quality Control, Sixth Edition, Mc Graw

Hill (2017)

2. Montgomery D C - Introduction to Statistical Quality Control : A Modern Introduction,

Wiley Student Edition (2015)

3. Gupta R C - Statistical Quality Control, Ninth Edition, Khanna Publishing Company (2001)

4. Mahajan M - Statistical Quality Control, Dhanpat Rai & Company Pvt. Ltd (2016)

5. Gupta S C and Kapoor V K - Applied Statistics, Sultan Chand and Sons (2014)

6. Bilal M Ayyub and Richard H McCuen - Probability, Statistics and Reliability for

Engineers and Scientists, Second Edition, Chapman and Hall (2010)

BOOKS FOR REFERENCE

1. Eugene L Grant and Richard S Leavenworth - Statistical Quality Control, Sixth Edition,

McGraw Hill Book Company (2017)

2. John, S Oakland and Followel R F - Statistical Process Control, Sixth Edition, John Oakland

(2012)

3. Rowland Caplen - A Practical Approach to Quality Control, Second Edition (1988)

4. Gerald M Smith - Statistical Process Control and Quality Improvement, Fifth Edition,

Pearson (2003)

5. Wetherill G B and Brown D W - Statistical Process Control: Theory and practice, Springer

(2013)

6. William Grant Ireson, Clyde F. Coombs and Richard Y. Moss - Handbook of Reliability

Engineering and Management, Second Edition, Mc Graw Hill (1996)

7. Sankaran Mahadevan and Achintya Haldar - Probability, Reliability and Statistical Methods

in Engineering Design, Wiley (2000)

http://www.amazon.com/exec/obidos/ASIN/0070127506/reliasoftcorpora

http://www.amazon.com/exec/obidos/ASIN/0070127506/reliasoftcorpora


2018 onwards

29

VI SEMESTER

THEORY PAPER VIII

ST8: OPERATIONS RESEARCH

Learning Outcomes

Introduction to Operations Research (OR) and Linear Programming Problem (LPP)


appreciate the meaning and scope of OR.

distinguish between the different types of models used in OR.

formulate a linear programming problem and solve it using graphical, simplex and big M

methods.

identify the feasible region if it exists; identify the nature of the solution.

Transportation and Assignment problems

Students will be able solve transportation and assignment problems and give the optimal

solution.

Decision Theory and Game Theory, PERT and CPM, Decision Trees


solve simple decision and game problems using different techniques.

to construct a simple network diagram; perform critical path calculation and PERT.

learn how to define a project in terms of activities such that a network can be used to describe

the project.

draw simple decision trees.

Inventory Theory, Queueing Theory and Simulation


describe an inventory system, simple inventory models and obtain mathematical solutions.

understand a queueing system and its different components; derive the characteristics of a single

server queue.

generate observations from different probability distributions.

appreciate the central limit theorem and law of large numbers.

Module I (08 hours)

Introduction to Operations Research and Linear Programming Problem

Unit 1

Definition and scope of operations research, phases and models in operations research, different

methods of deriving solution to the models.


2018 onwards

30

Unit 2

Definition of a linear programming problem (LPP), formulation and graphical solution of a LPP,

simplex procedure and Charnes‟ big M methods of solving a LPP, criteria for unique,

unbounded, multiple and infeasible solutions.

Module II (6 hours)

Transportation and Assignment Problems

Unit 1

Methods of finding initial basic feasible solution to a transportation problem by north-west

corner, matrix minima and Vogel‟s method, test for optimality by U-V method.

Unit 2

Introduction to assignment problem - mathematical formulation and Hungarian method of

finding the optimal solution; transportation and assignment problems as particular cases of LPP.


Decision Theory, Game Theory, PERT and CPM

Unit 1

Statistical decision problem, decision making under certainty, risk and uncertainty, maximin,

minimax, Laplace and expected payoff criteria, regret function, opportunity loss and expected

value of perfect information; construction of simple decision trees.

Unit 2

Introduction to game theory, basic terminology, two-person zero sum game, pure and mixed

strategies, solution of games with saddle point – minimax and maximin, dominance principle.

Graphical solutions for (2xn) and (mx2) games.

Unit 3

Project planning with CPM and PERT, drawing of project network, critical path calculations,

slack time and floats, PERT three estimate approach, calculation of probabilities of completing a

project within a specified period.


Inventory Theory, Queueing Theory, Simulation

Unit 1

Description of an inventory system, need, discussion of various inventory costs, demand and lead

time, buffer stock, reorder level; EOQ model with and without shortages, EOQ model with

quantity discounts (price breaks) – discussion of one price break.


2018 onwards

31

Unit 2

General description of a queueing system, elements and operating characteristics of a queueing

system, probability distributions used in M/M/1 queueing system, statement of steady state

probabilities of (M/M/1: ∞/FIFO) queueing system, derivation of expressions for queue length

and system size, waiting time in system and queue using Little‟s formula.

Unit 3

Introduction to simulation, advantages and limitations, Monte Carlo method, generation of random

observations from different theoretical distributions like binomial, Poisson, uniform, exponential,

gamma, normal and Cauchy and also from a given frequency distribution.

PRACTICAL - STP8

1. Formulation and Solution of LPP by Graphical Method

2. Solution of LPP by Simplex and Big M Methods

3. Transportation Problems

4. Assignment Problems

5. Decision Problems

6. Game Problems

7. Problems on CPM and PERT

8. Problems on EOQ Inventory Model

9. Problems on M|M|1 Queueing Model

BOOKS FOR STUDY

1. Goel B S, Mittal S K and Pundir S K - Operations Research, Thirtieth Edition, Pragathi

Prakashan (2018)

2. Taha H A – Operations Research : An Introduction, Tenth Edition, Pearson (2018)

3. Swarup Kanti, Gupta P K and Manmohan - Operations Research, Nineteenth Edition, Sultan

Chand & Sons (2017)

4. Natarajan A M, Balasubramani P, Tamilarasi A - Operations Research, Second Edition,

Pearson education (2014)

5. Mariappan P - Operations Research An Introduction, Pearson Education (2013)

6. Sharma J K - Operations Research Theory & Applications, Fifth Edition, Macmillan India

Limited (2012)

7. Sharma J K - Operations Research Problems and Solutions, Third Edition, Macmillan India

Limited (2012)

8. Sharma S D - Operations Research Theory, Methods & Applications, Fifteenth Edition

reprint, Kedar Nath Ram Nath (2017)


2018 onwards

32

BOOKS FOR REFERENCE

1. Anderson D R, Sweeney D J et al - Quantitative Methods for Business, Thirteenth

Edition, Cengage Learning Custom Publishing (2015)

2. Gillett B E - Introduction to Operations Research, Tata McGraw Hill Publishing

Company Limited (2012)

3. Hillier F S, Lieberman G J et al – Introduction to Operations Research, Tenth Edition,

McGraw Hill Education (2017)

4. Hira D S, Gupta P K – Operations Research, Revised Edition, Sultan Chand & Company

Ltd (2015)

5. Kapoor V K, Kapoor Sumant – Operations Research Quantitative Technique for

Management, Ninth Edition, Sultan Chand & Sons (2014).

6. Ravindran A, Phillips D T and Solberg J J- Operations Research: Principles and Practice,

Second Edition, Wiley India (2007)

7. Broson Richard, Naadimuthu Govindasami – Operations Research, Schaum‟s Outline

Series, Second Edition, McGraw Hill Education (2017)

8. Gass S I - Linear Programming: Methods and Applications, Fifth Edition, Dover

Publications (2010)

9. Mustafi C K - Operations Research Methods and Practice, Revised Third Edition, New

Age international Publishers (2006)

__________________________

Statistics Syllabus for B.Sc. - Mount Carmel College, Bangalore

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Transcript of Statistics Syllabus for B.Sc. - Mount Carmel College, Bangalore