28 The joint density function of two random losses X and Y i

28. The joint density function of two random losses X and Y is f(x, y) = { x + y, for 0

Solution

Joint density function is

f(x,y) = x+y

Let u,v= x, x-2y, u varies from 0 to 1 and v varies from 0 to -1

Transform x,y into u, v

Jacobian

1    1

0    -2    =-2

HEnce f(u,v) = -2(u+(u-v)/2)

= v-3u/2

Prob (V>0) = 0 as v varies from -1 to 0