Lec10 Geometric Distribution

# Lec10 Geometric Distribution - 1 Geometric Distribution...

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Geometric Distribution 1

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Geometric: Experiment and r.v. 2 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. R.v. X=number of trials to the first success X=2 X=6 X=5 X=4 X=3 X=1
Geometric: pdf, mean, variance 3 r.v. X = number of trials until the first success possible values X = 1, 2 . ... parameter p=P(success on a trial) mean and variance: X=1,2,…

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Ex: number of parts to first defective 4 The fraction of defective parts is 0.025. An inspector examines each part. She feels like the work is worthwhile when she finds a defective. What is prob of finding first defective on the 5th part. Ans: assume parts are independent. r.v. X = number of parts until the first defective r.v. X  geometric (p=P(“success”)=?) P(X=5) =P(ggggd)=.0226
5 Find probability of two defectives in a sample of 5 parts Find probability of three defectives in a row. Find probability that the first defectives is

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• Spring '12
• SUSANALBIN
• Probability theory, Geometric distribution, defective parts, defective rate, success possible values, defective r.v

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Lec10 Geometric Distribution - 1 Geometric Distribution...

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