HYPERGEOMETRIC DISTRIBUTION - Daniel Bezalel Garcia, John Marlo Nazareno.pptx
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Transcript of HYPERGEOMETRIC DISTRIBUTION - Daniel Bezalel Garcia, John Marlo Nazareno.pptx
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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$ity "istribution that describes the probability ofselecting from the k items labeledsuccesses and n-x failures from N-k
items labeled failures when a randomsample of size n is selected from N items.
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Hypergeometric Distribution
wherein,
- k is the total number of success in thepopulation.
- x is the total number of success whereyou are interested, success after n trials.
- N is the number of population.- n is the number of sampletrials deri!ed
from N
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Hypergeometric Distribution
PROPERTIES%
- A random sample of size n isselected without replacement from Nitems.
- #f the N items, k may be classi$edas success and N-K are classi$ed asfailures.
- No negati!e or positi!e connotation.
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8/18/2019 HYPERGEOMETRIC DISTRIBUTION - Daniel Bezalel Garcia, John Marlo Nazareno.pptx
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Hypergeometric Distribution
ME&N
• To 'n" t(e me#n o) t(e (ypergeometric"istribution* +e +rite t(e e,pecte" -#$ue #s*
• Bring out #$$ t(e const#nt -#$ues )rom t(esumm#tion #n" c#nce$ x +e get*
•
• /et y=x-1; x=y+1
• 0(en x=1; y=0
• x=n; y=n-1
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Hypergeometric Distribution
• Rec#$$ 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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Hypergeometric Distribution
1&RI&NCE
• To 'n" t(e -#ri#nce* +e +i$$ st#rtby getting t(e e,pecte" -#$ueo) *
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Using t(e s#me process inobt#ining t(e me#n*
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HypergeometricDistribution
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Hence*
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Simp$i)ying t(e e2u#tion*
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HypergeometricDistributionT(ere is #n interesting re$#tions(ip
bet+een t(e (ypergeometric "istributio#n" binomi#$ "istribution3 S#y* i) n is smcomp#re" to N, t(e n#ture o) t(e N item
c(#nges -ery $itt$e in e#c( "r#+3 So t(ebinomi#$ "istribution c#n be use" to#ppro,im#te t(e (ypergeometric"istribution +(en n is sm#$$ 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