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Statistics for Economics Question on Probability theory

Let X∼Normal (0, 1) and π‘Œ = |𝑋|. If the probability density function of π‘Œ is π‘“π‘Œ (y) then for 𝑦>0,Ο€2 \sqrt{\frac{\pi}{2}} π‘“π‘Œ (𝑦) is

A

eβˆ’y22e^{-\frac{y^2}{2}}

B

ey22e^{\frac{y^2}{2}}

C

eβˆ’y2e^{-y^2}

D

eβˆ’y2e^{-\frac{y}{2}}

Answer

eβˆ’y22e^{-\frac{y^2}{2}}

Explanation

Solution

The correct option is (A): eβˆ’y22e^{-\frac{y^2}{2}}