Consider a rectangle with sides of length S 1 and S 2 , where S 1 and S 2 are independent random...

Consider a rectangle with sides of length S₁ and S₂, where S₁ and S₂ are independent random variables. The probability distributions of S₁ and S₂ are

f_S1(s₁)= 2s₁,         0 ≤ s₁ ≤ 1

and

0 ≤ s₂ ≤ 4

(a) Find the joint distribution of the area of the rectangle A = S₁ S₂ and the random variable Y = S₁.

(b) Find the probability distribution of the area A of the rectangle.