A die is rolled once. If X is the number of ones and Y is the number of sixes obtained(note that each can have only two values, 0 or 1), find:

a. the expected value and variance of X and Y,

b. Cov(X, Y ).

answers (what ive done, can i get confirmation or suggestions?)

Since only one dice is rolled, expected value for E(X) and E(Y) would both be 1/6.

Since they are independent, E(XY) = 0

Var(x) = (1^2)/6 - (1/6)^2 = 5/36

Var(y) = 5/36

Cov(XY) = E(XY) - (μx)(μy) = 0 - (1/6)(1/6) = -1/36

is this right?