Problem 10

This is the archived version of this course from the Spring 2013 semester. You might find something more recent by visitning my teaching page.

# How many biased bits give an unbiased one?

Due: January 18
Points: 3

Supposed a coin is "biased" in that it gives heads with probability $$p$$ and tails with probability $$1-p$$, for some number $$0<p<1$$. For example, if $$p=.75$$, then the coin flip will come up heads (on average) three out of every four times.

Using the formula for Shannon entropy that we derived in class, determine how many times this $$p$$-biased coin must be flipped in order to equal the entropy in a single unbiased coin flip.