Question: Please show your work. Thanks 3. (13 points - Correctness) Entropy and expected coding length (a) (2 points - Correctness) Consider the following two distributions

Please show your work. Thanks 3. (13 points - Correctness) Entropy

Please show your work. Thanks

3. (13 points - Correctness) Entropy and expected coding length (a) (2 points - Correctness) Consider the following two distributions defined by the counts below, where the numbers represent the counts of 5 different values of a random variable. Distribution 1: (1,4,5,3,2) Distribution 2: (2,2,39,8,1) Which of the above two distributions has a higher entropy and why? You should NOT give the numerical entropy here (though you are welcome to compute it to check that your reasoning matches the math). Your explanation should be a qualitative argument. (b) (2 points - Correctness) Calculate the entropy for the given distribution. Show your work for full credit. Symbol Counts 12 6 3 3 6

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