1. Here is a list of symbol frequencies. (below)
Compute the bit length of the message obtained from it for:
a. a Huffman code
b. a Hu Tucker (order preserving) code
c. also, calculate the lower bound on bit length implied by Shannon’s Theorem,
d. give the Hu Tucker encoding defined by the symbol order of the frequencies below as well as a Huffman
2. Suppose we have a deck of cards that are numbered from 1 to n. We pick two of these at random. What is the expected difference between their numbers? Hint: use the fact that the expectation of a sum is the sum of the expectations, and use symmetry. Big hint: make this into a problem that has symmetry. Symmetry among what? What is there almost symmetry among already?
3. In a class of 80 what is the probability of no two students having the same birthday? (you may assume that nobody was born on feb 29, so there are 365 possible birthdays.)
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