Suppose that the dimensions X and Y of a rectangular metal plate may be considered to be independent continuous random variable with pdf's

X: g(x) = x 1, 1 < x 2

= x + 3, 2 < x < 3

= 0, elsewhere

Y: h(x) = 1/2 , 2 < y < 4

= 0, elsewhere

(a) Find the pdf of the area of the plate, A = XY

(b) Verify whether the pdf the random variable A is a legitimate pdf or not?

Solve both questions

Please correct the answer...