Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 60 / 2 / ii / a

Table of contents
- Solution a

Solution

The error indicator is a Bernoulli random variable with probabilities

P (Z = 1) = p_{e}

and

P (Z = 0) = 1 - p_{e}

. Its Shannon entropy is therefore the binary entropy

H (Z) = h (p_{e}) = - p_{e} lo g_{2} p_{e} - (1 - p_{e}) lo g_{2} (1 - p_{e}) .

Use

0 lo g_{2} 0 = 0

, so this expression also covers error probabilities zero and one.

 Ancestors (11)

 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