MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose we have binary channel from which we are able to receive zeroes and ones. We also know apriory probability $p$ of receiving "1". Then we can calculate information amount of each digit $q$ we receive:

q=0: $I=-\log_2(1-p)$ bits;

q=1: $I=-\log_2(p)$ bits.

Now imagine that the channel is "fussy": instead of receiving exact digits we receiving probability $q$ that transferred digit is "1". Previous example of "unfussy" channel is when $q$ can take only two values: $q\in\{0,1\}$.

What will be the amount of information of receiving probability $q$ given probability $p$?


share|cite|improve this question

closed as off-topic by Stefan Kohl, Venkataramana, Andrey Rekalo, Ricardo Andrade, Suvrit Jan 18 '14 at 5:08

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Stefan Kohl, Venkataramana, Andrey Rekalo, Ricardo Andrade, Suvrit
If this question can be reworded to fit the rules in the help center, please edit the question.

Not a research Q: read the FAQ – Anthony Quas Jun 22 '12 at 20:28
I have not found this question in the FAQ – Anton Sukhinov Jun 23 '12 at 18:41