Another question presented in lecture.

Consider a random variable (X,Y) which is uniformly distributed over the triangle T = {(x,y) | x > 0, y > 0, x+y < 9}.

a) Explain why X and Y are dependent (no calculations required).

b) Find f_y(y), the marginal pdf of Y. Check that it is a probability density.

c) For a fixed y ∈ (0,9), write down the set of values of x for which f_x|y=y (x|y) is non-zero.

d) Find f_x|y=y (x|y) over the range that you derived in part d.

e) Calculate Cov(X,Y).

Thanks!