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Questions › DSE › DSE 2018 › Q29
4 marks, −1Statistics › Random variables and standard distributions › Transformations and order statisticsHardabout 3 min

DSE 2018 Question 29: Random variables and standard distributions

Suppose YYY is a random variable with uniform distribution on the interval [−π/2,π/2][-\pi/2, \pi/2][−π/2,π/2]. The value of the (cumulative) distribution function of the random variable X=sin⁡YX = \sin YX=sinY at x∈[−1,1]x \in [-1, 1]x∈[−1,1] is

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Suppose Y is a random variable with uniform distribution on the interval [-π/2, π/2]. The value of the (cumulative) distribution function of the random variable X = sin Y at x ∈ [-1, 1] is (A) sin⁻¹(x)/π + 1/2 (B) sin⁻¹(x) + π/2 (C) sin⁻¹(x) + π (D) sin⁻¹(x)/π + π/2

Also written as: Suppose Y is a random variable with uniform distribution on the interval [-pi/2, pi/2]. The value of the (cumulative) distribution function of the random variable X = sin Y at x in [-1, 1] 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.

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Question from the DSE 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.