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(ex+y + e2x-y)
for 1 < x < 2 and 0 < y < 3, and f(x, y) = 0 elsewhere.
(a) What is the value of A?
(b) What is P(l.5 < X < 2, 1 < Y < 2)?
(c) Construct the marginal probability density functions fX(x) and fY(y).
(d) Are the random variables X and Y independent?
(e) If Y = 0, what is the conditional probability density function of X?