Question

An electronics store receives a shipment of 100 new processors. Unknown to the manager, 4 of these processors are defective. The manager randomly selects 5 of the processors and tests to see if they are defective. Let X be the number of defective processors that the manager finds. Find the pdf and cdf of X.

Answer 1

The PDF for the number of defective processors that the manager finds can be obtained here as:

P(X = x) = Number of ways to select x defective ones from 4 defective ones * Number of ways to select (5 - x) from 96 non defective ones / Total ways to select 5 processors from 100 processors

This is the required PDF for X here. The value of probabilities are computed using different values of X here as:

The CDF for X now is obtained as:

F(X < 0) = 0
F(X = 0) = 0.8119
F(X = 1) = P(X <= 1) = 0.8119 + 0.1765 = 0.9884
F(X = 2) = P(X <= 2) = 0.9884 + 0.0114 = 0.9998
F(X = 3) = P(X <= 3) = approx. 1
F(4) = 1