Do The Math Q17

Do The Math Q17

Claim amounts for wind damage to insured homes are independent random variables with common density function

where x is the amount of a claim in thousands.

Suppose 3 such claims will be made.

What is the expected value of the largest of the three claims?

  1. 2025 Correct Answer
  2. 2700
  3. 3232
  4. 3375
  5. 4500

Solution: A

First, observe that the distribution function of X is given by

Next, let X1, X2, and X3 denote the three claims made that have this distribution. Then if Y denotes the largest of these three claims, it follows that the distribution function of Y is given by

while the density function of Y is given by

Therefore