Take the tour ×  Suppose I have a file with random binary
strings of the same length in each line.  If I'm computing the
conditional entropy $H(Y|X)$ where $Y$ is the variable string of
fixed length $l$ which is after $X$, and $X$ is the variable
string of length $m$, and I find (lets say) $l=5$ and $m=10$
that the value of conditional entropy is $3$. Does that mean
that, given 10 bits, it is enough to predict 3 of the next to
fully recover the next 5 bits? Simpler asked: does that mean my
strings are not really randomly generated?  share|improve this
question add comment  1 Answer  up vote 1 down vote accepted  It
means that, given the 10 bits of $X$, then on average $Y$ has 3
bits of entropy (the average taken over the possible values of
$X$).  Thus, for your parameters, it does mean your strings are
not really randomly generated (they weren't drawn uniformly at
random from all possible strings of that length).  It doesn't
mean that given $X$, $Y$ will always have exactly 3 bits of
entropy, regardless of $X