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A memoryless source emits n symbols each with a probability p. The entropy of the source as a function of n

1. increases as log n
2. decreases as log (1/n)
3. increases as n
4. increases as n log n

Correct answer: increases as log n

Solution

The entropy of a memoryless source is related to the number of symbols it can emit, and as the number of symbols increases, the uncertainty or information content also increases, which is logarithmic in nature, hence it grows as log n.

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