LEC10 Geometric

# LEC10 Geometric - Geometric Distribution experiment Conduct...

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Geometric Distribution experiment: Conduct independent trials. The outcome on each trial is success with probability p and failure with probability 1-p. Stop at the first success. { } S = s, fs, ffs, fffs, ffffs, fffffs, . .. random variable: r.v. X = number of trials until the first success possible values X = 1, 2 . ... probability distribution function ( 29 f x P X x p p x ( ) ( ) = = = - - 1 1 x = 1,2 . ... parameter p=P(success on a trial) mean and variance: ( 29 E X p V X p p ( ) ( ) = = - 1 1 2

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until the first success The fraction of defective parts is 0.10. Find the probability of selecting 5 parts until the first defective. (First defective is on 5 th try.) r.v. X = number of parts until the first defective r.v. X geometric (p=P(“success”)=?) ( 29 f x x ( ) . . = - 9 1 1 x = 1,2 .... { } P X P ggggd ( ) . . . = = = = 5 9 1 0656 4 What is the probability that at least 3 good parts are selected until the first defective? ( 29
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LEC10 Geometric - Geometric Distribution experiment Conduct...

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