$[25$ pts$]($Proakis computer problem $12\mathrm{.}4)$ Huffman Code for Printed English: The probabilities of the letters of the alphabet occurring in printed English are given in the following table:

$\backslash$table$[[$Letter$,$Probability,Letter,Probability,Letter,Probability$],[A,0\mathrm{.}0642,B,0\mathrm{.}0127,C,0\mathrm{.}0218],[D,0\mathrm{.}0317,E,0\mathrm{.}1031,F,0\mathrm{.}0208],[G,0\mathrm{.}0152,H,0\mathrm{.}0467,$I,$0\mathrm{.}0575],[J,0\mathrm{.}0008,K,0\mathrm{.}0049,L,0\mathrm{.}0321],[$M$,0\mathrm{.}0198,N,0\mathrm{.}0574,O,0\mathrm{.}0632],[P,0\mathrm{.}0152,Q,0\mathrm{.}0008,R,0\mathrm{.}0484],[$S$,0\mathrm{.}0514,T,0\mathrm{.}0796,U,0\mathrm{.}0228],[V,0\mathrm{.}0083,W,0\mathrm{.}0175,x,0\mathrm{.}0013],[$Y$,0\mathrm{.}0164,Z,0\mathrm{.}0005,$Space,$0\mathrm{.}1859]]$

Use MATLAB to solve the following and add the code with your solutions. Hint: read documentation on 'huffmandict' function in MATLAB $($feel free to use other functions$/$language if you prefer$).$

$($a$)$ Determine the entropy from the given probabilities.

$($b$)$ Design a Huffman code using given probabilities.

$($c$)$ Determine the average code length and efficiency of the Huffman code.