An upright freezer is available in three different rated cap

An upright freezer is available in three different rated capacities: 16ft³, 18ft³, and 20ft³. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has pmf (for x=16, p(x) = 0.2), (for x=18, p(x) = 0.5), (for x=20, p(x) = 0.3)

a. Compute E(X), E(X²), and V(X)

b. If the price of a freezer having capacity X is 70X - 650, what is the expected price paid by the next customer to buy a freezer?

c. What is the variance of the price paid by the next customer?

Solution