Claim amounts for wind damage to insured homes are independent random variables with common density f(x) = ( 3 x4 , x > 1 0 , otherwise where x is amount of claim in thousands. (a) find the probability that a claim is below average? [19/27] (b) suppose 3 claims will be made. what is the expected value of the largest of the three claims? [2.025] (c) suppose 3 claims will be made. what is the expected value of smallest of the three claims? [1.125]

This distribution has expectation

a. The probability that falls below the average/expectation is

b. Denote by the largest of the three claims . Then the density of this maximum order statistic is

where is the distribution function for . This is given by

So we have

and the expectation is

c. Denote by the smallest of the three claims. has density

so the expectation is

step-by-step explanation:

use pothagarean therom

a^2+b^2=c^2 so first ac

acm is a right triangle because c= 90°

and am (the hypotenuse or c) =16+9 =25

but there is not enough info we need another angle or side length