Question Five A file contains the following characters with the frequencies as shown. If Huffman Coding is used for data compression, determine- a. Huffman Code for each character b. Average code length c. Length of Huffman encoded message (in bits) Question Six Calculate the entropy in bits for each of the following random variables: a. Pixel values in an image whose possible grey values are all the integers from 0 to 255 with uniform probability. b. Humans classified according to whether they are, or are not, mammals. c. Gender in a tri-sexed insect population whose three genders occur with probabilities 1/4,1/4, and 1/2. Question Seven a. Encode a binary word 11001 into the even parity hamming code. b. Let us assume the even parity hamming code from the above example is transmitted and the received code is (110001101). Detect and correct the error. Question Eight a Prove or disprove the set of codewords {10,010,101} is uniquely decodable b Let X be a discrete random variable on an alphabet of size five. Suppose the distribution of X is P=(1/4,1/4,p3,p4,p5), where the last three probabilities are unknown. Find the values of (p3,p4,p5) such that H(X) is maximized