Intro to Cryptography

This whole question is just one question as per Chegg policy.

4. The accuracy of a certain radio station's meteorologist at predicting rain is given bv the following chart Actually rains Does not actually rain Predicts rain 1/12 Predicts no rain 1/12 2/3 For example, the meteorologist predicts rain 1/12 of the time when in fact it does rain. Notice that the meteorologist is correct 3/4 of the time. (a) Compute the entropy of the probability distribution of the meteorologist's pre- dictions (b) An uninformed listener observes that they could be correct 5/6 of the time by simply always predicting no rain. Compute the entropy of the probability distri- bution of the listener's predictions. (c) The listener applies for the meteorologist's job. However, the station manager declines to hire the listener on the basis that the listener provides less information. What does this suggest about entropy as a measure of information