A discrete memoryless source has an alphabet of five symbols with their probabilities listed below Symbol: $2 S3 S4 Probability: 0.08 0.18 0.18 (a) [6 pts] Construct one Huffman code by placing the newly combined symbol to the highest place possible. (b) [2 pts] Draw the tree structure of the Huffman code derived from (a). (c) [2 pts] Calculate the average codelength of the Huffman code derived from (a). (d) [4 pts] Construct another Huffman code by placing the newly combined symbol to the lowest place possible. (e) [2 pts] Calculate the variance of the Huffman code derived from (d) SI 0.46 S5 0.1