You are testing each product out of a particular product run

You are testing each product out of a particular product run. Historically, the probability of a defective product is 2%. You are asked to test samples from the product run until a defective product is found.

What is the probability distribution for Y?

What is the mean and standard deviation for Y?

What is the probability that you will find a defective product by the 3^rd draw?

Solution

a. What is the probability distribution for Y?

Geometric distribution with p=0.02

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b. What is the mean and standard deviation for Y?

mean=1/p=1/0.02=50

standard deviation =sqrt((1-p)/p^2)=sqrt((1-0.02)/0.02^2) =49.49747

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c. What is the probability that you will find a defective product by the 3^rd draw?

(1-0.02)^2*0.02 =0.019208