Determine the value of c such that the function f(x,y) = cx²y for 0 < x < 3 and 0 < y < 2 satisfies the properties of a joint probability density function.

Determine the following:

(a) P(X <1, Y <1) 

(b) P(X <2.5)

(c) P(1

(d) P(X >2. 1

(e) E(X) 

(f) E(Y)

(g) Marginal probability distribution of the random variable X

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

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