# Information Theory- DMS question- Binomial dist?

1. Oct 16, 2012

### Zoe-b

1. The problem statement, all variables and given/known data
Let X1, . . . ,Xn be a message from a memoryless source, where Xi are in A. Show
that, as n →∞, the proportion of messages in the typical set converges to zero,
unless Xi is uniform on A.

2. Relevant equations

3. The attempt at a solution
Confused, possibly because I'm reading the question wrong.
Let B be a 'typical set' (proper subset of A), with P(Xi in B) = p

Then as far as I can tell, if Yn is the number of messages in B up to Xn, Yn has a Binomial (n,p) distribution and so the proportion of messages in B tends to p not to zero! But I'm not using how the actual 'letters' are distributed at all here, or the respective sizes of the sets A, B. Any hints?