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 < Y < 2.5)

d. P(X > 1.8, 1 < Y < 2.5)

e. E(X)

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

g. Marginal probability distribution of X