GATE 2014 EC (EC4) – Question 13
X is a zero-mean, unit-variance Gaussian random variable. Find $E[|X|]$.
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Correct answer: 0.79 to 0.81
Explanation
By symmetry,E|X|=2∫₀∞x exp(−x²/2)/√(2π)dx. The integral of xexp(−x²/2) over the positive half-line is1, giving E|X|=√(2/π)=**0.797885**. Zero mean gives E[X]=0but does not make the absolute mean zero.