Question

A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is Determine the probability that the portion of a claim representing damage to the house is less than 0.2.

Answer 1

Please find the complete question in the attachment.

Explanation:

The likelihood of the part of claims that is less than 0.05 for all the houses is calculated as:

`P(X < 0.05) = int^(0.05)_(0) int^(1-x)_(0) f(x,y) \ dy\ dx\\\\`

`= \int^(0.05)_(0) \int^(1-x)_(0) 6(1-x-y) \ dy\ dx\\\\= \int^(0.05)_(0) 6((1-x)-x(1-x)-((1-x)^2)/(2)) \ dx\\\\ = \int^(0.05)_(0) 6(1-2x+x^2-0.5-0.5x^2+x) \ dx\\\\= \int^(0.05)_(0) 6(0.5x^2-x+0.5) \ dx\\\\= 6(0.5* (0.05^3)/(3) -(0.05^2)/(2)+0.5 * 0.05 )\\\\ =0.1426\\\\`