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Questions › DSE › DSE 2010 › Q46
2 marksStatistics › Random variables and standard distributions › Transformations and order statisticsHardabout 4 min

DSE 2010 Question 46: Random variables and standard distributions

Suppose θ\thetaθ is a random variable with uniform distribution on [−π/2,π/2][-\pi/2,\pi/2][−π/2,π/2]. The value of the distribution function of the random variable X=sin⁡θX=\sin\thetaX=sinθ at x∈[−1,1]x\in[-1,1]x∈[−1,1] is

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

Also written as: Suppose theta is a random variable with uniform distribution on [-pi/2,pi/2]. The value of the distribution function of the random variable X=sin theta 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 2010 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.