 Weakly typical sequence

For an IID random variable source with probability mass function $p$, a word $x^n$ is weakly typical when $|-(1/n){\log }_{2}p(x^n)-H(X)|\le \epsilon$. It has probability on the scale $2^{-nH(X)}$. The weak law of large numbers makes the typical set probable, but does not make every word in it representative: for a uniform source every possible word is weakly typical.