An Appliance Dealer Sells Three Different Models of Upright Freezers $$\begin{array} { l c c c } \hline x & 13.5 & 15.9 & 19.1 \\\hline P ( x ) & .2 & .4 & .4 \\\hline\end{array}$$

question 3

Essay

An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf $$\begin{array} { l c c c } \hline x & 13.5 & 15.9 & 19.1 \\\hline P ( x ) & .2 & .4 & .4 \\\hline\end{array}$$
a. Compute $E ( X ) , E \left( x ^ { 2 } \right) , \text { and } V ( X )$
b. If the price of a freezer having capacity X cubic feet is 25X - 8.5, what is the expected price paid by the next customer to buy a freezer?
c. What is the variance of the price 25X - 8.5 paid by the next customer?
d. Suppose that although the rated capacity of a freezer is X, the actual capacity is $h ( X ) = X - .01 X ^ { 2 }$
What is the expected actual capacity of the freezer purchased by the next customer?

---

Definitions:

Unsecured Bond

A type of bond that is not backed by collateral, relying solely on the issuer's creditworthiness.

Secured Bond

A type of bond that is backed by collateral, providing greater assurance to the lender that principal and interest payments will be made.

Equity Bond

An investment instrument that combines features of both equity and debt, often structured to convert to equity under certain conditions.

Income Bond

A bond that pays interest to its holders only if the issuing company has earned enough profits to cover the interest payments.