The joint distribution of the random variable pair (X,Y) is the following:

f(x,y)=c(x2+y2)+xy.

when 01 and 0y1 and 0 otherwise.

a) Determine the constant c and the marginal distributions of the random variables X and Y.

b) Are the random variables X and Y independent?

c) Determine the conditional distribution XY=1 and the conditional expectation E(XY=1).