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Questions › IIT JAM › IIT JAM 2023 › Q28
2 marks, −0.667Statistics › Random variables and standard distributions › Transformations and order statisticsModerateabout 2 min

IIT JAM 2023 Question 28: Random variables and standard distributions

Let X∼Normal(0,1)X\sim\text{Normal}(0,1)X∼Normal(0,1) and Y=∣X∣Y=|X|Y=∣X∣. If the pdf of YYY is fY(y)f_Y(y)fY​(y), then for y>0y>0y>0, π2 fY(y)\sqrt{\tfrac{\pi}{2}}\,f_Y(y)2π​​fY​(y) is

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Let X~Normal(0,1) and Y=|X|. If the pdf of Y is f_Y(y), then for y>0, √(π/2) f_Y(y) is (A) e^(-y²/2) (B) e^(y²/2) (C) e^(-y²) (D) e^(-y/2)

Also written as: Let X~Normal(0,1) and Y=|X|. If the pdf of Y is f_Y(y), then for y>0, sqrt(pi/2) f_Y(y) is

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Transformations and order statistics, part of Random variables and standard distributions in Statistics.

The distribution of a function of a random variable, and of the largest or smallest of several.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

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Question from the IIT JAM 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.