Derivation of the probability distribution function of a binomial distributionby misogynisticfeminist Tags: binomial, derivation, distribution, function, probability 

#1
Mar2606, 03:24 AM

P: 387

Is there a way to derive
[tex] P (X=r) =^nC_r p^r q^{nr} , r= 0, 1, 2,...., n [/tex] where [tex] X: B(n,p) [/tex] where n is the total number of bernoulli experiments, p the probability of success q, the probability of failure. 



#2
Mar2606, 09:18 AM

Sci Advisor
HW Helper
P: 9,398

Yes, just think about it, it's just simple combinatorics (you omitted to mention independent trials, which is, I'm sure important), and no harder than working out how to choose r from n (in fact it is the same).




#3
Mar2906, 12:04 AM

PF Gold
P: 1,059

This is not a problem as matt goes into. Suppose we have XXX and YY,then how many ways can combinations occur? Well there are five elements in 5! ways, but 3 of them are similar and the other two are similar, so it's 5!/(3!2!)=10 distinct ways. YYXXX, YXYXX, YXXYX, YXXXY, XYXXY, XXYXY, XXXYY, XYYXX, XXYYX, XYXYX.



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