Question: A metal fabricating plant currently has five major pieces under contract, each with a deadline for completion. Let X be the number of pieces completed by their deadlines. Suppose that X is a random variable with PMF p(x) given by

x            0          1          2          3           4           5

p(x)      0.05      0.10      0.15     0.25      0.35        0.10

a) Compute the expected value and variance of X.

b) For each piece completed by the deadline, the plant receives a bonus of $15,000. Find the expected value and variance of the total bonus amount.