$[25$ pts$]($bonus$)$ A source has an alphabet $\{a_1,a_2,a_3,a_4\}$ with corresponding probabilities

$\{0\mathrm{.}1,0\mathrm{.}25,0\mathrm{.}3,0\mathrm{.}35\}.$

$($a$)$ Design a Huffman code for this source.

$($b$)$ Design a Huffman code for the second extension of the source $($take two letters at a time$).$

What is the average code word length? What is the average number of required binary

letters per each source output letter?