Consider the joint distribution of random variables X, Y and Z given on page 4 of the Lecture Set 4. Recall that we have shown in class that X and Y are conditionally independent given Z. (You can use a R-Code to perform the computations but be sure that you include the R code with your solution and show your reasoning). (a) Show that X and Y are not independent. (b) Compute correlation of X and Y . (c) Obtain the conditional distributions of Z given (X = 0, Y = 0) and (X = 1, Y = 1)