In: Statistics and Probability
please show all steps
Q.4 Let X and Y be continuous random variables with the joint pdf:
f(x, y) = { k(x + y), if (x, y) ∈ 0 ≤ y ≤ x ≤ 1 ; 0 otherwise
Answer the question with the equation below please
f(x, y) = 2(x + y), for 0 ≤ y ≤ x ≤ 1 and 0 otherwise.
(a) Find E[X + Y ] and E[X − Y ]
(b) Find E[XY ]
(c) Find E[ Y | X = x] and E[ X | Y = y].
(d) Find Cov[X, Y