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Questions › DSE › DSE 2020 › Q1
4 marks, −1Statistics › Random variables and standard distributions › Uniform distributionsModerateabout 3 min

DSE 2020 Question 1: Random variables and standard distributions

Consider independently and identically distributed random variables X1,…,XnX_1, \dots, X_nX1​,…,Xn​ with values in [0,2][0,2][0,2], each uniformly distributed on [0,2][0,2][0,2]. If Y=max⁡{X1,…,Xn}Y=\max\{X_1,\dots,X_n\}Y=max{X1​,…,Xn​}, then the mean of YYY is

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Consider independently and identically distributed random variables X₁, …, Xₙ with values in [0,2], each uniformly distributed on [0,2]. If Y=max {X₁,…,Xₙ}, then the mean of Y is (A) [n/(n+1)]² (B) n/2(n+1) (C) 2n/(n+1) (D) n/(n+1)

Also written as: Consider independently and identically distributed random variables X_1,..., X_n with values in [0,2], each uniformly distributed on [0,2]. If Y=max {X_1,...,X_n}, then the mean of 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 Uniform distributions, part of Random variables and standard distributions in Statistics.

Equally likely outcomes over a finite set or an interval.

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.