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

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

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

(a) $85 (b) $163 (c) $168 (d) $213 (e) $255