Answer Happy

A box has 4 balls, labeled from 1 to 4. One ball is

selected from the box. On the trial, Xavier wins 1 dollar if the label of the selected ball is either 1 or 2 but wins nothing otherwise. Similarly, Yoshi wins 1 dollar if the label of the selected ball is either 3 or 4, but wins nothing, otherwise. Zoe wins 1 dollar if the label of the selected ball is either 2 or 3 but wins nothing otherwise. Let X, Y, and Z denote the amounts (in dollars) won by Xavier, Yoshi, and Zoe, respectively, on the one trial.

Determine the value of Pr(X=1, Y=0, Z=1).

Determine the means and variances of X, Y, and Z. E[X] = = EY] = E[Z) = = 2 Var(X) = , Var(Y) = = Var(Z) = Show your work.

Find Cov(X,Y) and Cov(X,Z). Cov(X,Y) = Cov(X,Z) = = Show your work.