Consider 12 independent rolls of a 6-sided die. Let X be the number of 1's and let Y be the number of Ts obtained. Compute

*E[*

*X],*

*E[*

*Y],*Var(X), Var(Y),

*E[X*Y], Var(X Y), Coy (X, Y), and

*p(X,*Y). (Hint: You may want to compute the in the order given.)

I answered the following :

*E[*

*X] = np = 12 * 1/6 = 2*

*E[*

*Y] = 2 (same as above)*

Var(X) = np(1-p) = 5/3

Var(Y) =5/3 (same as above)

*E[X +*Y] = E(X) + E[Y] = 4

Var(X + Y) = Var(X) + Var(Y) = 10/3 (independent variables)

Cov (X, Y) = E(XY) - E(X+Y) = ? - 4

*p(X,*Y) No idea

are my answers correct?