hypergeometric distribution - daniel bezalel garcia, john marlo nazareno.pptx

8/18/2019 HYPERGEOMETRIC DISTRIBUTION - Daniel Bezalel Garcia, John Marlo Nazareno.pptx

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HYPERGEOMETRIC

DISTRIBUTION

Daniel Bezalel A. Garcia

Marlo Nazareno


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Hypergeometric Distribution

DEINITION

! Hypergeometric distribution is a"iscrete prob#bi$ity "istribution that describes the probability ofselecting from the k items labeledsuccesses and n-x failures from N-k

items labeled failures when a randomsample of size n is selected from N items.


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wherein,

- k is the total number of success in thepopulation.

- x is the total number of success whereyou are interested, success after n trials.

- N is the number of population.- n is the number of sampletrials deri!ed

from N

•


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PROPERTIES%

- A random sample of size n isselected without replacement from Nitems.

- #f the N items, k may be classi$edas success and N-K are classi$ed asfailures.

- No negati!e or positi!e connotation.


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ME&N

• To 'n" t(e me#n o) t(e (ypergeometric"istribution* +e +rite t(e e,pecte" -#$ue #s*

• Bring out #$$ t(e const#nt -#$ues )rom t(esumm#tion #n" c#nce$ x +e get*

•

• /et y=x-1; x=y+1

• 0(en x=1; y=0

• x=n; y=n-1

•


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• Rec#$$ t(e Binomi#$!Mu$tinomi#$T(eorem +(ic( st#tes t(#t*

• T(en a = k-1, b = N-k, m = n-1#n" t(#t is*

•

•


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1&RI&NCE

• To 'n" t(e -#ri#nce* +e +i$$ st#rtby getting t(e e,pecte" -#$ueo) *

•

Using t(e s#me process inobt#ining t(e me#n*

•


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HypergeometricDistribution

•

Hence*

•

Simp$i)ying t(e e2u#tion*

•


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HypergeometricDistributionT(ere is #n interesting re$#tions(ip

bet+een t(e (ypergeometric "istributio#n" binomi#$ "istribution3 S#y* i) n is smcomp#re" to N, t(e n#ture o) t(e N item

c(#nges -ery $itt$e in e#c( "r#+3 So t(ebinomi#$ "istribution c#n be use" to#ppro,im#te t(e (ypergeometric"istribution +(en n is sm#$$ comp#re" t

In )#ct* t(e #ppro,im#tion is goo" +(enT(us* i) +e set * t(en t(e me#n o) t(e

(ypergeometric "istribution coinci"es +t(e me#n o) t(e binomi#$ "istribution* #

t(e -#ri#nce o) t(e (ypergeometric


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HypergeometricDistributionE4&MP/E

%ots of &' components each areconsidered unacceptable if theycontain ' or more defecti!es. (heprocedure for sampling a lot is toselect )* components at random and

re+ect the lot if defecti!e was found.hat is the probability of e-actly )defecti!e is found in the sample if

there are ' defecti!es in the entire lot

hypergeometric distribution - daniel bezalel garcia, john marlo nazareno.pptx

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