# Exam P Practice Problem 53 – Hospital Expense Plans

Problem 53-A

An insurer sells a hospital expense plan that pays a fixed sum per day of hospitalization. Suppose that the number of days of hospitalization in a year for someone insured under this plan has a Poisson distribution with mean 0.8.

In each calendar year, the plan pays 2,000 for each day of hospitalization subject to the condition that the first two days of hospitalization are the responsibilities of the insured.

What is the expected payment for hospitalization during a calendar year under this hospital expense plan?

$\displaystyle (A) \ \ \ \ \ \ \ 116.24$

$\displaystyle (B) \ \ \ \ \ \ \ 244.75$

$\displaystyle (C) \ \ \ \ \ \ \ 305.93$

$\displaystyle (D) \ \ \ \ \ \ \ 785.26$

$\displaystyle (E) \ \ \ \ \ \ \ 1600.00$

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Problem 53-B

An insurer sells a hospital expense plan that pays a fixed sum per day of hospitalization. Suppose that the number of days of hospitalization in a year for someone insured under this plan has the following probability function.

$\displaystyle P(X=x)=\frac{3}{4^{x+1}} \ \ \ \ \ \ \ \ x=0,1,2,3,\cdots$

In each calendar year, the plan pays 1,000 for each day of hospitalization subject to the condition that the first day of hospitalization is the responsibility of the insured.

What is the expected payment for hospitalization during a calendar year under this hospital expense plan?

$\displaystyle (A) \ \ \ \ \ \ \ 76.83$

$\displaystyle (B) \ \ \ \ \ \ \ 83.33$

$\displaystyle (C) \ \ \ \ \ \ \ 111.11$

$\displaystyle (D) \ \ \ \ \ \ \ 145.83$

$\displaystyle (E) \ \ \ \ \ \ \ 333.33$

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