GATE EC 2020 Set 1 — Question 32
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Communications → Information Theory → Information Measure & Entropy
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Question
A binary random variable takes the value or . The probability . The value of (rounded off to one decimal place), for which the entropy of is maximum, is ______.
Correct answer
0.5 to 0.5
Solution
The entropy of a binary random variable with probabilities and is given by:The entropy is maximum when the outcomes are equally likely, which occurs when:Thus, the value of for maximum entropy is .
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