Claim amounts for wind damage to insured homes are independent random variables with common density function f(x) = 3x −4 for x > 1, and f(x) = 0 otherwise, where x is the amount of a claim in thousands. Suppose 3 such claims are made. What is the expected value of the largest of the three claims?

The expected value of the largest of the three claims is $ 2025.00

Step-by-step explanation:

To solve the question, if we have the three claims given by

C₁, C₂, C₃ and the let the maximum claim be denoted by M = max(C₁, C₂, C₃)

If the expected value of M is expressed as E(M) and the common density function is F(m)  with p,d,f f(m) = F'(m) of M

Therefore, F(m) = P (max C₁, C₂, C₃) ≤ M) = P (C₁ ≤m) ×  P (C₂ ≤m) × P (C₃ ≤m)

=  

From which

F'(m) = =

E(M) =

Which gives

=

= 9× = $ 2.025 × 10³

=$ 2025.00