2. [1+1+2+3+1+1=9 points] 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. Compute the (a) Huffman code, (b) Average code word length in bits/symbol. (b) Let the source be extended to order two. Apply the Huffman algorithm to the resulting extended source, and now compute the (a) Huffman code (b) Average code-word length of the new code in bits/symbol. (c) Compare the average code-word length calculated in part (b) with the entropy of the original source. In part (c), you need to realize the upper and lower bounds of the average codeword length (upper and lower bounded by Entropy terms)