$(2)$ For the following list of letter frequencies, create a Huffman tree, and use it to determine the encoding for each of the letters. After you've written down the encoding for each letter, determine the average number of bits needed to encode ANY letter using this encoding. $(15$ pts$.)$

A: $\mathrm{.}33$ B: $\mathrm{.}10$ C: $\mathrm{.}08$ D: $\mathrm{.}12$ E: $\mathrm{.}37$