# what is relative entropy between to random binary string with length of $L_1$ & $L_2$?

I want calculate relative entropy between two strings of binary such as:

$L_1:11000100011101001$
$L_2:00101110110111001$
It is primarily when the lengths of two strings is same and in general when the length is not same. and how calculate $p$ and $q$. Is it related to frequency in string or need infer from some more general distribution or what?
For example what is the $q$ and $p$ here?

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Relative entropy is defined between two probability distributions. If you only have samples, you'll need to define a probability distribution and then estimate relative entropy. Is this a homework? –  Memming Nov 5 '13 at 2:46