Question: A random variable X takes on three values, e.g., a, b, and c, with probabilities 0.55, 0.25, and 0.2. (a) What are the lengths

A random variable X takes on three values, e.g., a, b, and c, with probabilities 0.55, 0.25, and 0.2. (a) What are the lengths of the binary Huffman codewords for X? What are the lengths of the binary Shannon codewords for X? [4 marks] (b) What is the smallest integer D such that the expected Shannon codeword length with a D-ary alphabet equals the expected Huffman codeword length with a D-ary alphabet? [3 marks] (c) Here X and X are independent with each other and take on three values, e.g., a, b, and c, with probabilities 0.55, 0.25, and 0.2. We define Y = XX2, e.g., Y = ab if X = a and X = b. Find the binary Huffman codewords for Y. [5 marks]

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