Question

An insurance company models the number of warranty claims in a week on a particular product that has a Poisson distribution with mean 4. Each warranty claim results in a payment of 1 by the insurer. Calculate the expected total payment by the insurer on the warranty claims in a week.

Answer 1

4 monetary units

Explanation:

In a Poisson distribution, the expected value of the distribution is the same as the mean:

`E(X)=\mu=4\ claims`

The expected number of warranty claims is 4.

Since each claim results in a payment of 1, the expected value paid by the insurer is:

`E(V)=E(X)*V(X)\\E(V)=4*1 = 4`

The expected total payment on warranty claims is 4 monetary units.