Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 224 / 3 / a

Table of contents
- Solution a

Solution

The type of

x_{1}^{n} \in A^{n}

is its empirical mass function

P_{x_{1}^{n}} (a) = \frac{1}{n} \sum_{i = 1}^{n} 1_{{x_{i} = a}}, a \in A .

For a product source

Q^{\otimes n}

,

Q^{\otimes n} (x_{1}^{n}) = i = 1 \prod n Q (x_{i}) = a \in A \prod Q (a)^{n P_{x_{1}^{n}} (a)} = 2^{- n {H (P_{x_{1}^{n}}) + D (P_{x_{1}^{n}} ∥ Q)}},

with the usual convention that the probability is zero if the string uses a symbol outside the support of

Q

.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version