Question

3. Multiple Choice Question Consider the discrete random variables X and Y with the following joint probability mass function: y fxy(x,y) -1 0 1/8 0 -1 1/4 0 0 1/8 -1 1 1/8 -1 1/8 Given that X is not negative, what is the probability that Y is also not negative? 1 1 A. 0.5 B. 0.8 C. 0.4 D. 0.25 E. none of the preceding

Answer 1

P(Y is not negative | X is not negative) = P(Y is not negative and X is not negative) / P(X is not negative)

P(Y is not negative and X is not negative) = P(Y = 1, X = 0) + P(Y = 0, X = 1) = 1/4 + 1/8 = 3/8

P(X is not negative) = P(X = 0, Y = -1) + P(X = 0, Y = 1) + P(X = 1, Y = 0) + P(X = 1, Y = -1) = 1/4 + 1/4 + 1/8 + 1/8 = 3/4

Hence, the required probability, P(Y is not negative | X is not negative) = (3/8) / (3/4) = 0.5

Option (A) is the correct choice.