all info are provided in the question, also I put it in computer science category, Why it's in advanced math category?

. . a d Problem 4 (20 points) a) (3 pts) Which of the following cannot be correct Huffman encodings? Justify your answer by drawing the corresponding Huffman trees and point to possible mistakes. {ab, ba {a, ba, bb} {a, ba, ab, bb {aa, ab, ba, bba) b) Consider the following table showing the frequency of various letter in a file. Letter b Frequency 20% 40% 20% 10% 10% Encoding 01 1 000 0010 0011 (3 pts) Prof. Dimitriou came up with an encoding for each character which is shown above. Is this a valid encoding that could have been produced by the Huffman algorithm? Explain. (4 pts) Come up with a different Huffman tree whose height is three. Show your work. To ease grading, when combining trees always pick the smallest letter(s) or the subtree(s) containing the smallest letter(s). (2 pts) Compute the average length of each encoding for the 5 characters. Are they the same? (4 pts) Encode the sequence bacbab with Prof. Dimitriou's encoding. Suppose now the first bit is received in error. How many characters will be wrong during the decoding process? Do the same for your encoding. What happens in this case? (4 pts) Repeat the above assuming the 3rd bit is flipped during transmission. Is one of the encodings better than the other with respect to wrong decoded characters