An appliance dealer sells three different models of freezers

An appliance dealer sells three different models of freezers with advertised capacity of 13, 16 and 20 cubic feet. Let X = the amount of storage space of the freezer purchased by the next customer.

PMF of X is below

x 13 16 20

p(x) .2 .5 .3

a) The price of a freezer having cubic capacity X is given by 25X – 20. What are the expected value and variance of the price paid by the next customer?

b) Suppose that although the advertised capacity of a freezer is X, the actual capacity is h(X) = X – 0.01 X^2. What are the expected value and variance of h(X), the actual capacity of the freezer bought by the next customer?

Solution