Consider a discrete memoryless source with alphabet {s0, s1, s2} and statistics {0.7, 0.15, 0.15} for its output.

a. Apply the Huffman algorithm to this source. Hence, show that the average codeword length of the Huffman code equals 1.3 bits/symbol.

b. Let the source be extended to order two. Apply the Huffman algorithm to the resulting extended source and show that the average codeword length of the new code equals 1.1975 bits/symbol.

c. Extend the order of the extended source to three and reapply the Huffman algorithm; hence, calculate the average codeword length.

d. Compare the average codeword length calculated in parts b and c with the entropy of the original source.