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

Determine the following:

(a) P(X <1, Y <2) 

(b) P(1< X <2)

(c) P(Y >1) 

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

(e) E(X) 

(f) V (X)

(g) Marginal probability distribution of X

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

(i) E(Y | X = 1) 

(j) P(Y >2 | X = 1)

(k) Conditional probability distribution of X given that Y = 2