An insurance company will insure a $50,000 diamond for its fullvalue against the

Question

An insurance company will insure a $50,000 diamond for its fullvalue against theft at a premium of $400 per year. Suppose that theprobability that the diamond will be stolen is .005, and let xdenote the insurance company’s profit.
a) What is the name of this distribution? Circle the correctanswer.
A) Discrete Distribution. B) Sampling Distribution about theMean
C) Normal Distribution D) Binomial Distribution
b) Set up the probability distribution of the random variable x intabular form.
c) Calculate the insurance company’s expected profit.
d) Find the yearly premium that the insurance company should chargeif it wants its expected profit to be $1,000.

Explanation / Answer

A) DiscreteDistribution

x

P(X = x)

$400

0.995

-$50,000

0.005

E(X) = xP(X = x) = $400 * 0.995 - $50,000 * 0.005= $148

E(X) = xP(X = x) = $a * 0.995 - $50,000 * 0.005 =$1,000

Let a = the new premium in order to yield a profit to$1,000.

x

P(X = x)

$400

0.995

-$50,000

0.005

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