Let and be two independent tosses of a fair coin. Find the entropy and the joint entropy . Why is ?
Consider an unfair coin where the two outcomes, heads and tails, have probabilities and .
If the coin is flipped two times, what are the possible outcomes along with their respective probabilities?
Show that the entropy in part (a) is . How could this have been predicted without calculating the probabilities in part (a)?
A random variable takes the values with probabilities . Calculate the entropy .
Let be a random variable taking on integer values. The probability is 1/2 that is in the range