GATE 2020 EC – Question 32
A binary random variable $X$ takes the value $+2$ or $-2$. The probability $P(X=+2)=\alpha$. The value of $\alpha$ (rounded off to one decimal place), for which the entropy of $X$ is maximum, is ________.
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Correct answer: 0.49 to 0.51
Explanation
The entropy $H=-\alpha\log\alpha-(1-\alpha)\log(1-\alpha)$ of a binary variable is largest when both outcomes are equally likely, so $\alpha=0.5$.