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

If the patient is to receive $200 from an insurance company 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?

Solution:

Step 1 of 2:

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

f(x) = , x= 1,2,3,4.

If the patient will receive $200 from the insurance company for each of the first two days in the hospital. And $100 for each of the remaining days. We have to find the expected payment of the patient.