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Unformatted text preview: Chapter 4 Section 4: Geometric Distribution Page 232-233 You have a Bernoulli experiment, except you only sample until you get your first success. X = the number of trials needed until you get the first success. Notation: X Geom( p ) where p is the probability of success pmf for the Geometric Distribution f ( x ) = p (1- p ) x- 1 for x = 1 , 2 , 3 , . . . otherwise cdf for the Geometric Distribution F ( x ) = P ( X x ) = 1- (1- p ) x Mean and Variance of Geometric Distribution Mean: E( X ) = for all x xf ( x ) = 1 p Variance: Var( X ) = for all x x 2 f ( x )- 2 = 1- p p 2 Ex. A particularly biased coin, when tossed, will come up heads 75% of the time. Assume that trials are independent. Let X = the number of the tosses that results in the first head. (a) What is the pmf of X ? (b) Find the probability that exactly three trials are required to get the first head....
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