Let X and Y have joint density fXY (x; y) = c(x + y)^2 for 0 x 1; 0y1. (a) Determine c. (b) Find the marginal distribution of X. (c) Find the...

Let X and Y have joint density fXY (x; y) = c(x + y)^2 for 0≤ x ≤1; 0≤y≤1.(a) Determine c.(b) Find the marginal distribution of X.(c) Find the conditional density fY|X(y|x).(d) Calculate the conditional expectation E(Y |X = x).