Lec09 Binomial Distribution

# Lec09 Binomial Distribution - 1 Binomial Distribution 2...

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Binomial Distribution 1

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Binomial Distribution: the Situation 2 Experiment There are N independent trials. The outcome for each trial is success with probability p and failure with probability 1-p. Define r.v. X = number of successes in N independent trials Possible values of X: 0,1,2,…,N
Binomial pdf 3 parameters: 0<p<1 and N mean and var: E(X) = Np V(X)=Np(1-p)

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The combination notation 4 1 0 and )! ( ! ! N 0,1,. .., = x ) 1 ( ) ( ) ( = - = - = = = - N x N x N x N where p p x N x X P x f x N x
Ex: Computing Binomial Probabilities 5 The prob a student receives a good dorm lottery number is 0.6. Four roomates want to be together. r.v. X = number of successes in 4 independent trials X Binomial (N=4, p=P(success)=.6) Find prob 2 have good numbers. Find prob at least 2 have good numbers

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Understanding the pdf for Binomial 6 r.v. X = number of successes in 4 independent trials
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Lec09 Binomial Distribution - 1 Binomial Distribution 2...

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