Exercise 2.14 - A measure of correlation

For question (a), we only have to borrow the conclusion from Exercise 2.12.:

For question (b), we have $0\le r\le 1$ in question b for $I(X;Y)\ge 0$ and $H(X|Y)\ge 0$.

For question (c), $r=0$ iff $X$ and $Y$ are independent so the distance between $p(x,y)$ and $p(x)\cdot p(y)$ is zero regarding KL-divergence.

For question (d), $r=1$ iff $X$ is determined by, but not necessarily equal to, $Y$.