If ten fair six-sided dice are rolled, suppose that X is the total number of even numbers shown and Y is the total number of fives shown.
(a) What is the joint p.m.f. of X and Y ?
(b) What is the marginal variance of X? Can you answer this question in one line, using an argument that does not involve any summation?
I found for (a) that f(x,y) = ((1/2)^x)*((1/6)^y)*((1/3)^(10-x-y))*10!/(x!y!(10-x-y)!).
But I really don't know how to approach (b). How can you tell the marginal variance of X without doing all of the summations?