Question: Let there be a system having 10 discrete energy levels, from 1 to 10. Let N be the digit sum of your student ID. E.g.,

Let there be a system having 10 discrete energy levels, from 1 to 10. Let N be the digit sum of your student ID. E.g., if your SID = 1155012345, then N = 27. Let pi = Ni/N for i = 1 to 10 be the probability that the system is at an energy level i, and Ni equals the i-th digit in your SID. E.g., p9 = 4/27 in this case.

Calculate the Shannon entropy of the system and show your steps in a necessary detail such that I can know you get the answer by yourself (e.g., not by running a computer program written by someone else).

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