Bab VI. Variabel Acak

8/16/2019 Bab VI. Variabel Acak

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VARIABEL

ACAK OLEH :

FATMA ARFAN, ST


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Defnisi Variabel Acak

•Variabel acak aala!"ariabel #an$ nilain#a

i%en%&kan 'le! !asil(erc'baan acak)


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Variabel Acak Terba$i * :

•Variabel

Acak Diskri%

•VariabelAcakK'n%in#&


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Variabel Acak

Diskri%


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Defnisi Variabel Acak Diskri%

Variabel acak iskri%aala! "ariabel acak#an$ nilain#a a(a%

dihitung)


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C'n%'!: Variabel Acak Diskri%

• +&la! 'bil #an$ %er-&al i seb&a! ealer (aa b&lan

%er%en%&

• +&la! r&a! (aa s&a%& bl'k

• +&la! ikan #an$ %er%an$ka( (aa l'ba eancin$

ikan

• +&la! k'(lain #an$ i%eria seb&a! kan%'r

(enerban$an (aa !ari %er%en%&

• +&la! nasaba! #an$ ena%an$i bank (aa -a

%er%en%&)


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Dis%rib&si Variabel Acak Diskri%

• Aala! seb&a! %abel a%a& r&&s #an$ encan%&kanse&a ke&n$kinan nilai "ariabel acak iskri% an nilai(el&an$n#a

x P(x)

0

12

¼

2/4¼


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C'n%'! :./ Ten%&kan r&&s is%rib&si (el&an$ ban#akn#a sisi

$abar bila seb&a! &an$ l'$a ile(ar 0 kali)B&a%la! %abeln#a 1

Eksperimen :

(ele(aran . a%a &an$ 02, Ban#akn#a %i%ik sa(el3 *0 3 4

S 35AAA, AA6, A66, 666, A6A, 6A6, 6AA, 66A7


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Ban#akn#a &nc&l sisi $abar aala!

+ai 8&n$si (el&an$ aala! :

9n%&k 2 3 ,.,*,0

Tabel is%rib&si (el&an$ :

JumlahGambar

0 1 2 3

F;2/ .


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.


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*/ Seb&a! a& ile(arkan *2

Misalkan : 2 3 -&la! %i%ik a& ala ke&a le(aran i%&, aka

2 3 *, 0, >, ?, @, , 4, , ., .., .*

Tabel is%rib&si (r'babili%as 2 :

a/ =;24/ 3 =;23/=;23./=;23../ =;23.*/

3 >


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Variabel Acak

K'n%in#&


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Defnisi Variabel Acak K'n%in#&

•Variabel acakk'n%in#& aala!"ariabel #an$

nilain#aen$an&n$ satu

interval a%a& lebih


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Dis%rib&si Variabel Acak K'n%in#&

•Dis%rib&si ini secarak'nse(%&al saa en$an

is%rib&si "ariabel acakiskri%, !an#a alais%rib&si ini ki%a en$&k&r(r'babili%as alaren%an$


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•Misaln#a : aala! %in$$i baan #an$

i&k&r ala sa%&an INCI,ke&ian ki%a in$inen$!i%&n$ %in$$i baansese'ran$ %erle%ak alain%er"al, ka%akanla! an%ara

@G@4 inci)


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• =r'babili%as %in$$i sese'ran$ ala in%er"al @G@4 inciin#a%akan seba$ai aera! #an$ iarsir)

K e ( a a % a n

( r ' b a b i l i % a s

@4@ Tin$$i baan ala inci

=r'babili%as %in$$i baan%erle%ak an%ara @ an @4

inci


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Karak%eris%ikDis%rib&si

=r'babili%as


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Karak%eris%ikDis%rib&si =r'babili%as

•Nilai Hara(an

;E2(ec%e Val&e/•Varians

•S%anar De"iasi


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Nilai Hara(an ;E2(ec%e Val&e/

• +&la! !asil kali ari nilaiGnilai "ariabel acak %erseb&%

en$an (r'babili%asn#aasin$Gasin$)

•Nilai Hara(an iseb&% -&$anilai ra%aGra%a ;ean/


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Nilai Hara(an ;E2(ec%e Val&e/

• x = E;/ 3

28;/

2


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C'n%'! :

Angka yang Muncul Probabilias Angka xProbabilias

2 F;2/ 8;2/

. .


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SIFATGSIFAT EKS=EKTASI

./ E;a/ 3 a*/ E;b2/ 3 b)E;2/

0/ E;2a/ 3 E;2/ a>/ E;b2a/ 3 b)E;2/ a

?/ E;c2* b2a/ 3 c)E;2*/

b)E;2/ a


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VARIANS

• Mer&(akan nilai !ara(an ari selisi! k&ara% an%araasin$Gasin$ nilai en$an nilai !ara(an a%a& nilai

ra%aGra%an#a)

• Men&n-&kkan (en#ebaran asin$Gasin$ nilai iseki%ar nilai !ara(an< nilai ra%aGra%an#a)


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VARIANS

aau

aau


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STANDAR DEVIASI

• Mer&(akan akar k&ara% #an$ ('si%i8 ari VARIANS)


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Si8a%Gsi8a% :


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C'n%'! :

.) Dike%a!&i : is%rib&si (r'babili%as sbb :

Hi%&n$ :a/ Mean 2

b/ Variansi 2

c/ De"iasi s%anar 2

/ / +ika # 3 >2G*, !i%&n$ : E;#/, "ar;#/ Ds;#/


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+aJab :

c/ Ds ;2/ 3 3 .,04

/ # 3 >2 *

E;#/ 3 E;>2G*/ Var ;#/ 3 "ar;>2G*/

3 >)E;2/ * 3 >)"ar;2/ 3 >);0,0/ * 3 >);.,./

3 .0,* * 3 ,@>

3 ..,*

Ds;#/ 3 Ds;>2G*/

3 >)Ds;2/

3 >);.,04/ 3 ?,?*


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T96AS MANDIRI . :

*) Seb&a! a%a &an$ ile(ar seban#ak 0 kali) Berik&%is%rib&si (r'babili%as kel&arn#a &ka ;M/

Hi%&n$la! :

a/ Mean E;2/

b/ Variansi ;/

c/ S%anar e"iasi


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T96AS MANDIRI . :

0) Se'ran$ (e%ani in$in e&%&skan a(aka! iaakan enana (ai a%a& %iak, karena aan#akeara& #an$ c&k&( (an-an$)

Bila ia e&%&skan akan enana (ai akaakan en$!asilkan beras seban#ak *,? %'nen$an !ar$a -&al (er k$ R() >,G)

%e%a(i bila !&-an %iak %&r&n aka (e%ani

%erseb&% en$alai ker&$ian sebesar R()?),G karena (anenn#a $a$al)

Bila (r'babili%asn#a akan %&r&n !&-an 3 ,>)

+ika (e%ani e&%&skan enana (ai, a(aka!

en$&n%&n$kan a%a& %iak1


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T96AS MANDIRI . :

>) Se'ran$ cal'n (en$&sa!a e(&n#ai !ara(an&n%&k e(er'le! ke&n%&n$an se%ia( b&lann#a

R() *?),G)

=r'babili%as (en$&sa!a %erseb&% e(er'le!ke&n%&n$an 3 ,@ ser%a besarn#a ke&n%&n$an #an$i(er'le! R() ?),G

Bera(aka! ker&$ian #an$ &n$kin ieri%an#aseanain#a ia %e%a( en$!ara(kan ke&n%&n$an se%ia(b&lann#a R() *?),G


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Bab VI. Variabel Acak

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