Problem 10 Suppose that the joint density function of the random variables X and Y is given by F(x,y) = {1 elsewhere a) Compute P(X + Y < 1).(Sketch the region clearly.) b) Find the marginal density of X, i.e. fx(x) and marginal density of Y, i.e. fy (y). c) Find the conditional density of Y given X, that is, fyix (1) d) Find the conditional expectation of Y given X, that is, E[YIX=]