Lecture 5 : Lower Bounds using Information Theory Tools

We begin by examining balanced vs. unbalanced coins, where the coins stand for statistical assumptions. Assume we have two coins, a balanced coin r with distribution r0 = 1 2 and r1 = 1 2 , and an unbalanced coin p with distribution p1 = 1 2 + and p0 = 1 2 − . This scenario is equivalent to the inspection of a given assumption, trying to figure out whether it is random or better than random. We will now investigate the behavior of m coin flips over P and R. Lemma 5.2.1 For m random variables independently sampled, it holds that