A stock solution of hydrochloric acid (HCl) supplied by a certain vendor contains small amounts of several impurities, including copper and nickel. Let X denote the amount of copper and let Y denote the amount of nickel, in parts per ten million, in a randomly selected bottle of solution. Assume that the joint probability density function of X and Y is given by: f(x, y) = c(x+y)^2 0 < x < 1 and 0 < y < 1
0 Otherwise

Required:
a. Find the value of the constant c so that f(x, y) is a joint density function.
b. Compute the marginal density function fX (x).
c. Compute the conditional density function fY|X (y|x).
d. Compute the conditional expectation E(Y| X = 0.4).
e. Are X and Y independent? Explain.