Determine the value of c that makes the function f (x, y) = ce^{− 2x− 3y} a joint probability density function over the range 0 < x and 0 < y < x.

Determine the following:

(a) P(X <1, Y <2) 

(b) P(1< X <2)

(c) P(Y >3) 

(d) P(X < 2,Y < 2)

(e) E(X) 

(f) E(Y)

(g) Marginal probability distribution of X

(h) Conditional probability distribution of Y given X = 1

(i) E(Y | X = 1)

(j) Conditional probability distribution of X given Y = 2