# Conditional entropy

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?

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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 $X$).
It doesn't mean that given $X$, $Y$ will always have exactly 3 bits of entropy, regardless of $X$. The amount of entropy in $Y$ might depend upon the specific value of $X$ you are given. Example: it might be that if you're given $X=0000000000$, $Y$ has 2 bits of entropy, but if you're given $X=1111111111$, $Y$ has 4 bits of entropy.