Chapter 2.2, Problem 5E

Let the random variable X be the number of days that a certain patient needs to be in the hospital. Suppose X has the pmf

$f\left(x\right)=\frac{5-x}{10},x=1,2,3,4$.

If the patient is to receive $200 from an insurance comp any for each of the first two days in the hospital and $100 for each day after the first two days, what is the expected payment for the hospitalization?