Question

An optical inspection system is used to distinguish among different part types. The probability of correct classification of any part is 0.98. Suppose that three parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. Determine the probability mass function and cumulative mass function of X.

Answer 1

Let , X be the number of parts that are correctly classified.

Here , X has binomial distribution with parameter n=3 and p=0.98

q=1-p=1-0.98=0.02

Therefore , the probability mass function of X is ,

; x=0,1,2,.......,n

= 0 ; otherwise

The table for the probability mass function and cumulative mass function of X is given below ,

X	0	1	2	3	Total
P(X=x)					1.00
F(x)	0.0000	0.0000+0.0012=0.0012	0.0012+0.0576=0.0588	0.0588+0.9412=1.00