Solve the following problem:
A discrete memory less source produces outputs {a1, a2, a3, a4, a5, a6}. The corresponding output probabilities are 0.7, 0.1, 0.1, 0.05, 0.04, and 0.01.
1. Design a binary Huffman code for the source. Find the average codeword length. Compare it to the minimum possible average codeword length.
2. Is it possible to transmit this source reliably at a rate of 1.5 bits per source symbol? Why?
3. Is it possible to transmit the source at a rate of 1.5 bits per source symbol employing the Huffman code designed in part 1?