Q. 5 Once a fire is reported to a fire insurance company, the company makes an initial estimate, X, of the amount it will pay to the claimant for the fire loss. When the claim is finally settled, the...

How i can solve (iii)

Extracted text: Q. 5 Once a fire is reported to a fire insurance company, the company makes an initial estimate, X, of the amount it will pay to the claimant for the fire loss. When the claim is finally settled, the company pays an amount, Y, to the claimant. The company has determined that X and Y have the joint probability density function 2 fx.y(x, y) = x2(x – 1) ex-15/&-D); x > 1,y > 1 0; e. w. (i) Show that it is a joint probability density function; (ii) Find cumulative distribution function Fx,y (x, y); (iii) Find the following probabilities (a) P(X > 1, Y > 1), (b) P(X > Y), (c) P(X + Y > 1)