I have the following question:
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?
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?