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# Lecturenotes9 - STAT 430/510 Lecture 9 STAT 430/510...

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STAT 430/510 Lecture 9 STAT 430/510 Probability Hui Nie Lecture 9 June 9th, 2009

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STAT 430/510 Lecture 9 Review Discrete Random Variables Expected Value and Variance Binomial Random Variable Poisson Random Variable
STAT 430/510 Lecture 9 Geometric Random Variable X is said to be a geometric random variable with parameter p if its pmf is given by P ( X = n ) = ( 1 - p ) n - 1 p , n = 1 , 2 , ··· X represent the number of trials until getting one success. Each trial is independent with success probability p .

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STAT 430/510 Lecture 9 Example X=number of tosses of a fair coin until getting a head. The pmf of X is P ( X = n ) = 0 . 5 n - 1 × 0 . 5 X is a geometric random variable with parameter 0.5
Example An urn contains N white and M black balls. Balls are randomly selected, one at a time, until a black ball is obtained. If we assume that each selected ball is replaced before the next one is drawn, what is the probability that (a) Exactly n draws are needed? (b) At least

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Lecturenotes9 - STAT 430/510 Lecture 9 STAT 430/510...

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