The file characterFreqs.mat contains a vector with $27$ entries, corresponding to the approximate relative frequencies of the letters $`\text{'}-`$z$\text{'}($plus the whitespace$)$ in common English text$\mathrm{.}1$ Note that the entries in the vector characterFreqs sum to $1.$

$($a$)$ Imagine a source that randomly generated characters $($independently$,$ one after another$)$ according to the pmf defined by characterFreqs. What is the entropy of this source?

$($b$)$ Construct a Huffman code for this source. Show your work. What is the average number number of bits this Huffman code would

require to encode the source described in part $($a$)?$