Question: Given RV's $X$ and $Y$ with ranges $\{0, 1, 2\}$ and $\{0, 1\}$, how large can $I(X;Y)$ be?
Attempt at Solution:
I know that $I(X;Y)$ is less than or equal to $H(X)$, so I am assuming that if I calculate $H(X)$, then I'll know the maximum value that $I(X;Y)$ can be. If I'm just given the range of $X$, then should I just assume that each $X$ value has a probability of $\frac{1}{3}$, since there are $3$ $X$ values? I'm not even sure if I'm thinking about this correctly...
Thank you in advance!