Problem 5 (6) A supermarket manager is interested in the relationship between X = the number of times a sale item is advertised in the local newspaper and the demand for the item. Let Y be the demand with the value of 0 for low demand, 1 for moderate demand and 2 for high demand. The manager estimated the joint probabilities for demand and advertising shown below XY O 1 2 1 0.09 0.15 0.06 2 0.1 0.36 0.24 a) Find the probability distribution of Y. (3) b) Compute P(X = 1|Y = 2). Are X and Y independent random variables? (Justify your answer) (3)