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.