Suppose that X and Y have a discrete joint distribution for which the probability distribution is defined as follows: P(x,y) = c |x + y| for x = -2, -1, 0, 1, 2 and y = -2, -1, 0, 1, 2; = 0 otherwise.

(a) Determine the value of the constant c.

(b) Compute P(X = 0 and Y = −2)

(c) Compute P(X=1)

(d) Compute P(|X − Y | ≤ 1)

(e) Compute the conditional probability distribution, P(Y |X = 1).

(f) Obtain the conditional mean of Y given X = 1, that is, E(Y |X = 1)