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) Geometric distribution with p=0.02

B) we have to find the mean and standard deviation for Y

   we know that mean of geometric distribution is given by E(Y)=1/p

hence mean =1/0.02=50   answer

and also Standerd deviation =square root of (varience)

varience =(1-p)/p²

var(Y) =0.98/0.0004=2450

then standerd deviation=square root(2450)=49.50(approx) answer

C) we have to find P(Y=3)

since P(Y=k)=(1-p)^k-1*p

then

P(Y=3)=(0.98)²0.02=0.019208 answer