When thinking about typical sets, I've been coming across the notion of the 'typical probability':
(1) $p_{typical, X} = 2^{-H(X)}$
(2) $H(X) = -\Sigma p_{i}log(p_{i})$ = $-\Sigma log(p_{i}^{p_{i}})$
For more of an example, see Section 1 here: http://en.wikipedia.org/wiki/Typical_set
When we actually plug (2) into (1), we get:
(3) $p_{typical, X} = \Pi p_{i}^{p_{i}}$.
I'm trying to figure out if there's a way to intuitively understand (3). I know we can keep just thinking of it as some number a few algebraic steps from (1), but is there some deeper intuition that relates it to the pdf?
Thanks.