Claim amounts for wind damage to insured homes are independent random variables with common density function
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.34.1.jpg)
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
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.34.2.jpg)
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
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.34.3.jpg)
while the density function of Y is given by
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.34.4.jpg)
Therefore
![](https://www.beanactuary.org/wp-content/uploads/2020/10/eq.34.5.jpg)