"unil- nil-I Question 1 Let X and. Y be discrete random variables with joint frequencies Show in Table 1 below: (b) (C) y X 0'1'T'3-4 a 14 a 14 s 4 1 7 5 s 9 6 2 9 12 6 12 2 3 6 s 16 2 4 Table 1 With clear workings, evaluate (Le. compute) the following probabilities: i) PU! > 1.? = 3), ii)P(X a 2.Y2 j=e and P(Y=1.X=0)+P(Y=1.X=1)+P(Y=1.X=2)+P(Y=1,X=3) What do you observe about the two terms? Explain the rationale behind your observation(s). (10 marks) Discuss the steps you would implement to calculate E [Y|X S 1]. What are some practical applications of conditional expectations? (10 marks) \"4,..- AJ...:._:._4.-...-t.' kl I _|_