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Chapter 6: Q.10 (page 354)

Fire insurance Suppose a homeowner spends \(300for a home insurance policy that will pay out \)200,000if the home is destroyed by fire. Let Y=the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is 0.0002.

(a) Make a table that shows the probability distribution of Y.

(b) Compute the expected value of Y. Explain what this result means for the insurance company

Short Answer

Expert verified
  1. The probability distribution of Yis

Y($)199700300Probability0.00020.9998

b. The expected value ofY is$260.

Step by step solution

01

Part (a) Step 1: Given Information

Given in the question that,

Amount spend on insurance =$300

Amount insurance will pay if fire destroys home =$200000

Probability that fire will destroy the home=0.0002

02

Part (a) Step 2: Calculation 

Using the given information, the probability distribution is:

Y300-200000300Probability0.00021-0.0002

The probability distribution is

Y($)199700300Probability0.00020.9998

03

Part (b) Step 1: Given Information

Given in the question that,

Amount spend on insurance=$300

Amount insurance will pay if fire destroys home =$200000

Probability that fire will destroy the home=0.0002

04

Part (b) Step 2: Calculation 

The expected value can be computed using the following formula:

E(Y)=∑y×P(y)=300(0.9998)+(−199700)(0.0002)=260

The insurance company's estimated profit per homeowner is$260.

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