Chapter 8.5, Problem 38E

Hospitalization Insurance    An insurance policy pays an individual $100 per day for up to 3 days of hospitalization and $25 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function

     $P\left(X=k\right)=\{\begin{array}{cc}\frac{6-k}{15}& \text{for}k=1,2,3,4,5\\ 0& \text{otherwise}\text{.}\end{array}$

Calculate the expected payment for hospitalization under this policy. Choose one of the following. Source: Society of Actullries.

1. (a) $85
2. (b) $163
3. (c) $168
4. (d) $213
5. (e) S255