The objective of this problem is to design and develop a program for Huffman coding algorithm. The discrete source has an alphabet X = {x1, x2, x3, x4, x5, x6, x7, x8, x9} with corresponding probabilities, P = {0.2, 0.15, 0.13, 0.12, 0.1, 0.09, 0.08, 0.07, 0.06}. (a). Solving the problems below by hands (without programming) Design a Huffman code and sketch the corresponding code tree. Specify the Huffman codes for the nine symbols in the alphabet. Determine the average code length of the Huffman code. Determine the entropy of the source and compare it with the average codeword length of the Huffman code. Is there any difference (redundancy)?