The Shannon entropy of a source $X$ (in bits) is defined as:-
$$ H(X) = -\sum_{x \in X} {p(x) \log_2 p(x)} $$
Following principles in Variance of Area and Average Estimators in Monte Carlo Estimation of Pi and Having an empirical chart, what is the probability that the mean of a 99,000 sized set of bytes is $\le 127$? ,is it possible to determine the variance of $H(X)$ for any $X$?
