319.2. The following is a probability matrix for X = {1, 2, 3} and Y = {1, 2, 3}; i.e., the Joint Prob (X = 3, Y = 2) = 18.0%:

x _ **1** **2****3** _ y _ **1** _ 6% 15% 9% _ **2** _ 12% 30% 18% _ **3** _ 2% 5% 3%

Each of the following is true EXCEPT which is false? a. X and Y are independent b. The covariance(X,Y) is non-zero c. The probability Y = 3 conditional on X = 1 is 10.0%; i.e., Prob (Y = 3, X = 1) = 10.0% d. The unconditional probability that X = 2 is 50.0%; i.e., Prob (X = 2) = 50.0%

What is the reason for X and Y to be independent ?, and what if Prob(x=1,y=1) = 0 % or 100 %

Regards

GN