Chapter 9.1, Problem 32E

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
78 views

Insurance An insurance company needs to determine the annual premium required to break even for collision protection for cars with a value of $10,000. The random variable x is the claim size on these policies, and the analysis is restricted to the losses$1000, $5000, and$10,000. The probability distribution of x is as shown in the table. What premium should customers be charged for the company to break even? x 0 1000 5000 10,000 P(x) 0.936 0.040 0.020 0.004

To determine

To calculate: The annual premium which should be charged from customers by the insurance company in order to break even on cars with a face value of $10,000. Explanation Given Information: The probability distribution of claim size of these policies:  Claim size (x)in$ 0 1000 5000 10,000 Probability 0.936 0.04 0.02 0.004

Formula used:

If x is a discrete random variable which assumes values x1,x2,x3,......,xn with respective probabilities P1,P2,P3.......Pn then the expected value or mean X¯ is defined as E(X)=X¯=P1X1+P2X2+P3X3+.....+PnXn=i=1nP1X1.

Calculation:

Consider the given probability distribution table can be represented as

 X 0 1,000 5,000 10,000 P(X) 0.936 0.040 0.020 0.004

Where, X, P(X) represents claim and their respective probability, where for

X1=0X2=1000X3=5000X4=10000

And

P(x)=P1=0.936P(x)=P2=0.040P(x)=P3=0.020P(x)=P4=0.004

Consider the formula for expected value E(X)=X¯=P1X1+P2X2+P3X3+

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