Hello

I need your help please about probability question.

pleas take a look

QUBStiOR 4 : The chart below shows the joint probability func tion of two discrete random variables X and Y, each having possible outcomes 1,20r 3. Y:1 Y:2 Y:3 X=1 1/8 1/8 1/8 X=2 1/8 1/8 1/8 X=3 1/8 1/8 0 (a) Find the (discrete) probability functions of X and of Y by listing all their values (or by a table]. (b) Find ]E(X) and 130/). (c) Find Var(X) and Var(Y). (d) Find all possible outcomes of the random variable Z : X Y. (e) Find the probability function of Z and ]E(Z). (f) Find Cov(X,Y). (g) Find the correlation coefcient p(X, Y). (h) Can you give an intuitive explanation of the sign of the correlation by only arguing with the values in the above chart of the joint probability function? In other words, could you have predicted the sign of p(X, Y) before starting to work any of the parts of this