1
vote
1answer
60 views

Maximising Entropy of Random Variable taking Positive Integer Values

A random variable $X$ takes positive integer values and $E[X]=6$. What distribution of the random variable $X$ maximises the entropy $H(X)$? What if $X$ can only take a finite number of values? ...
2
votes
0answers
36 views

How to prove the function is logarithmic with coefficience

I am given a set of properties for an unknown function $f(x)$. In particular, not constantly zero, not negative, additive and continues for any $x$ between 0 and 1. I am asked to show equivalence ...
0
votes
1answer
141 views

Entropy Problem: mutual information

I have a problem about entropy and mutual information that I have attempted, but would like feedback on. 30% Boas 20% Anaconda 50% Cobra Half of the Cobras were medium sized, and the other half were ...
0
votes
0answers
73 views

entropy of perfect cryptosystems

I am working on the product of two perfect crypto-systems and I need to prove that the product is secure. $$a -- [\text{system}\ 1] -- b -- [\text{system}\ 2] -- c$$ How can I prove that $H(a) = ...