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Consider a source with 5 possible messages: a1, a2, a3, as, as. (a) What is the maximum possible entropy for a source of this type (that is, a source with 5 possible messages)? (b) Suppose this source generates its message according to the following probability distri- bution: P(a)= 0.24, P(a2) = 0.22, P(a3) = 0.20, P(as) = 0.18, P(as) = 0.16. How many bits would a Huffman code assign to message a3?

Consider a source with 5 possible messages: a1, a2, a3, as, as. (a) What is the maximum possible entropy for a source of this type (that is, a source with 5 possible messages)? (b) Suppose this source generates its message according to the following probability distri- bution: P(a)= 0.24, P(a2) = 0.22, P(a3) = 0.20, P(as) = 0.18, P(as) = 0.16. How many bits would a Huffman code assign to message a3?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Consider a source with 5 possible messages: a1, a2, a3, a4, a5. (a) What is the maximum possible entropy for a source of this type (that is, a source with 5 possible messages)? (b) Suppose this source generates its message according to the following probability distri- bution: P(a)= 0.24, P(a2) = 0.22, P(a3) = 0.20, P(as) = 0.18, P(as) = 0.16. How many bits would a Huffman code assign to message a3?
Transcribed Image Text:Consider a source with 5 possible messages: a1, a2, a3, a4, a5. (a) What is the maximum possible entropy for a source of this type (that is, a source with 5 possible messages)? (b) Suppose this source generates its message according to the following probability distri- bution: P(a)= 0.24, P(a2) = 0.22, P(a3) = 0.20, P(as) = 0.18, P(as) = 0.16. How many bits would a Huffman code assign to message a3?
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