Question

The annual premium of a special kind of insurance starts at $10000 and is reduced by 10% after each year where no claim has been filed. The probability that a claim is filed in a given year is 0.07, independently of preceding years. What is the PMF of the total premium paid up to and including the year when the first claim is filed?

Answer 1

`P(X=x)= \sum_(y=1)^(x)1000*(90)/(100)*0.93`

Explanation:

Given the:

The annual premium of special kind of insurance starts at $1000 and reduced by 10% after each year where no claimed has been filed.

Also give that the claim is filed in given year is 0.07, independently of preceding years.

The PMF of the total premium paid upto and including the year when first claim is led

`P(X=x)= \sum_(y=1)^(x)1000*(90)/(100)*0.93`