I'm trying to find the expected value, variance, and cdf of getting doubles when throwing 2 dice. So the set that I want to represent is {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}.
I calculated the expected value (E(X)) = 1/6 The variance (Var(X)) = 5/36
However, how do I calculate the CDF of x for specific dice throws such as getting doubles?
Let $X$ be a random variable representing the number of doubles in one roll of two dice. Then the cdf of $X$ is defined by $$F(x)=\Pr(X\leq x)$$ so that $$F(0) = \frac56\\F(1)=1$$
I don't think it's customary to have the domain of the cdf of a discrete random variable be the real numbers, as you seem to do in your comment, but if we wanted to, we could write $$G(x)=\cases{0,& x<0\\ \frac56,& $0\leq x$ < 1\\1,& $x\geq1$}$$