Consider a discrete memory less 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 code word length of the l-Iuffm.an 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 code-word length of the new code equals 1.1975 bits/symbol.

(c) Compare the average code-word length calculated in part (b) with the entropy of the original source.