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Homework Help: Information Theory- DMS question- Binomial dist?

  1. Oct 16, 2012 #1
    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?
  2. jcsd
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