Question

An insurance policy pays 100 per day up to 3 days of hospitalization and 50 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function ��=� ={ policy.

Answer 1

Letting $X$ denote the number of days in the hospital, and $Y$ the total payment, the given information can be summarized in the following table: 

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c} k & 1 & 2 & 3 & 4 & 5 \\ \hline P(X=k) & 5/15 & 4/15 &3/15 & 2/15 & 1/15 \\ \hdashline Y & 100 & 200 & 300 & 350 & 400 \\ \end{array}$$

$$P(Y)=100(\dfrac{5}{15})+200(\dfrac{4}{15})+300(\dfrac{3}{15})$$

$$+350(\dfrac{2}{15})+400(\dfrac{1}{15})=220$$

The the expected payment for hospitalization under this policy is 220.