Suppose that two continuous random variables X and Y have a joint probability density function f(x, y)

Question:

Suppose that two continuous random variables X and Y have a joint probability density function
f(x, y) = A(x-3)y
for -2 < x < 3 and 4 < y < 6, and f(x, y) = 0 elsewhere.
(a) What is the value of A?
(b) What is P(0 < X < 1,4 < Y < 5)?
(c) Construct the marginal probability density functions fX(x) and fY(y).
(d) Are the random variables X and Y independent?
(e) If Y = 5, what is the conditional probability density function of X?