Question

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(x) = 5-x/10, x=1, 2, 3, 4. 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?

Answer 1

To calculate the expected payment for the hospitalization, multiply each possible number of days by its corresponding probability and payment amount. Then, sum up the results. In this case, the expected payment is $170.

Step-by-step explanation:

To calculate the expected payment for the hospitalization, we need to multiply each possible number of days by its corresponding probability and the corresponding payment amount for those days.

1. For x=1, the payment is $200 and the probability is f(1) = 5-1/10 = 0.4.
2. For x=2, the payment is $200 and the probability is f(2) = 5-2/10 = 0.3.
3. For x=3, the payment is $100 and the probability is f(3) = 5-3/10 = 0.2.
4. For x=4, the payment is $100 and the probability is f(4) = 5-4/10 = 0.1.

Now, we can calculate the expected payment by multiplying each payment amount with its probability and summing them up:

Expected payment = ($200 * 0.4) + ($200 * 0.3) + ($100 * 0.2) + ($100 * 0.1) = $80 + $60 + $20 + $10 = $170.