Tagged Questions

46 views

Compressing binary numbers

If I have a arbitrarily long random binary number with the condition that the probability that a given digit is 0 and 1 is 1/4 and 3/4, respectively. What is the best way to compress this into a ...
31 views

What connections between computer science and ergodic theory?

I have a background in ergodic theory, but I am switching to computer science/programming. I would like to know if tools from ergodic theory could be useful, especially something around coding of ...
87 views

Which takes more energy: Shuffling a sorted deck or sorting a shuffled one?

You have an array of length $n$ containing $n$ distinct elements. You have access to a comparator on the elements (a black-box function that takes $a$ and $b$ and returns true if $a < b$, false ...
161 views

Prove that entropy is maximized when probability is $1/n$

How can be proven that the entropy of a dice roll is maximized when the probability of each of its $6$ faces is equal, $1/6$?
86 views

Conditional entropy of sum of random variables

How can be proven that for random variables $A$ and $B$, and $C = A + B$, $$H(C\mid A) = H(B\mid A).$$ Also, would it be possible to determine if $H(C)$ would be greater than $H(A)$?
The inherent unpredictability, or randomness, of a probability distribution can be measured by the extent to which it is possible to compress data drawn from that distribution.  \text{more ...