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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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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 0.040 0.020 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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