A random variable X takes on three values, e.g., a, b, and c, with probabilities 0.55,...

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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 X₁ and X₂ 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 = X₁X2, e.g., Y = ab if X₁ = a and X₂ = b. Find the binary Huffman codewords for Y. [5 marks] 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 X₁ and X₂ 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 = X₁X2, e.g., Y = ab if X₁ = a and X₂ = b. Find the binary Huffman codewords for Y. [5 marks]

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a To find the lengths of binary Huffman codewords and binary Shannon codewords for the random variable X with probabilities 055 a 025 b and 02 c you c... View the full answer