Question

Can someone explain where the 1!,4!,2!,5!, etc is coming from?


Hypergeometric Probability Distribution QA=D_64)(3) _G)G). G).|5121) f(x) = W (13) .4773 12! 3!9! 220

Answer 1

Explanation

Hypergeometric distribution

The hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size N that contains exactly objects with that feature, wherein each draw is either a success or a failure.

f(x) which is provided in the question is its pmf - Probability mass function

In its pmf, COMBINATION IDENTITIES are used.

They can also be written as nCr. Formula for calculating combination is written in the attached file.

Factorial

Combination identities are expanded or solved using factorials which work in following way.

n! = n*(n-1)*(n-2)*........*1

6! = 6*5*4*3*2*1

Please see the attached 2 files.

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In given distribution Problem, combination identities are working as fe) = (2) Nr "xx WCn-x hore or NCn N 26 Since combination is used in typergeometrisc distribution - Now, we put values- (1) CS, X7G 1263 12 3 using commentity combination 51 15-1)! X_7 21x6-2)! n! ner (n-)! X 12! 3! (2-3) sxy! 7x6x5! |х М 2x1x & "12 x 11x10xg! 342x1 gr = los 5 X 21 = -9773 ya hany 220 220 CSScanned with CamScanner

"Cr= (2) no r= To Calculate combinations, we use the formula n! r!(n-1)! whore n= ofitems no of items being chosen at a time. Example If A boy x chooses 3 mories out of to movies, then n will be 10 fr will be 3. 10 Cz oo 101 3! (0-3)! 3*7! lox 8x8x7 120 42X1X so, he could select 120 different combination of 3 movies out of those 10 movies. so, nca ( 10! 3 1 C&Scanned with CamScanner