Exercise An assembly Consists of three mechanical components

Exercise An assembly Consists of three mechanical components. Suppose that the probabilities that the first, the second and the third components meet the specifications arc 0.92, 0.94 and 0.93. Assume that the components are independent. Let the random variable X denote the number of components in the assembly meet the specifications. Determine mean and variance of X.

Solution

A: First component works. B: Second component works. C: Third component works.

The probability that x is 3, which is the probability that all 3 components work ,

= P(A and B and C) = P(A)*P(B)*P(C) = .92*.94*.93 = 0.804264

The probability that x is 2, which is the probability that exactly 2 components work,

= P(A and B) + P(B and C) + P(A and C)