1. Huffman encoding improved. The problem has to show improving of the average length of the code-word by applying the Huffman algorithm to pairs of letters instead of single letters 1.1 Consider the information source S fX, Y, Z? with probabilities P 10.1,0.2,0.7 Create the Huffman tree and the give corresponding Huffman encoding. For the Huffman encoding calculate the entropy, the average number of bits and the efficiency of the encoding 1.2. Consider now the information source S-XXXYXZ,YX,YY,YZ, ZX,ZY,ZZj. The probabilities of all those nine pairs are based on the given probabilities P 0.1,0.2,0.7), but now they are computed by multiplying probabilities of both letters. For example, the probability ofXX 0.1 * 0.1-0.01, XY-0.1*0.2 0.02 and so on. Create the Huffman tree and give corresponding Huffman encoding. For the Huffman encoding calculate the entropy, the average number of bits and the efficiency of the encoding