Determine the value of c such that the function f (x, y) = cxy for 0 < x < 3 and 0 < y < 3 satisfies the properties of a joint probability density function.

Determine the following:

(a) P(X <2, Y <3) 

(b) P(X <2.5)

(c) P(1

(d) P(X >1.8, 1

(e) E(X) 

(f) P(X <0, Y < 4)

(g) Marginal probability distribution of X

(h) Conditional probability distribution of Y given that X =1 5 .

(i) E(Y | X) = 1.5) 

(j) P(Y <2 | X = 1.5)

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