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Let $X$, $Y$ be discrete random variables taking values within the same set of $N$ elements. Let the total variation distance $|P-Q|$ (which is half the $L_1$ distance between the distributions of $P$ ...

I have $n$ IID Bernoulli random variables denoted by $X_1,X_2,\ldots X_n$ with parameter $p$. I am interested in knowing if the following inequality involving mutual information holds : $\boxed{\max_{...