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?
- 2025 Correct Answer
- 2700
- 3232
- 3375
- 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
