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Questions › DSE › DSE 2011 › Q33
2 marksStatistics › Random variables and standard distributions › Transformations and order statisticsModerateabout 3 min

DSE 2011 Question 33: Random variables and standard distributions

Suppose XXX and YYY are independent random variables that follow the uniform distribution on the interval [0,1][0,1][0,1]. Let Z=min⁡{X,Y}Z=\min\{X,Y\}Z=min{X,Y}. Pr⁡(Z<0.5)\Pr(Z<0.5)Pr(Z<0.5) (the probability that ZZZ is less than 0.5) equals

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Suppose X and Y are independent random variables that follow the uniform distribution on the interval [0,1]. Let Z=min {X,Y}. Pr (Z<0.5) (the probability that Z is less than 0.5) equals (A) 0.25 (B) 0.5 (C) 0.625 (D) 0.75

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 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.