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Questions › DSE › DSE 2014 › Q42
2 marks, −0.666666666666667Statistics › Random variables and standard distributions › Geometric and hypergeometric distributionsHardabout 3 min

DSE 2014 Question 42: Random variables and standard distributions

Ms A selects XXX from Uniform[0,1][0,1][0,1]. Mr B repeatedly and independently draws Y1,Y2,…Y_1,Y_2,\dotsY1​,Y2​,… from Uniform[0,1][0,1][0,1] until he gets a number larger than X/2X/2X/2, then stops. The expected number of draws that Mr B makes equals

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Ms A selects X from Uniform [0,1]. Mr B repeatedly and independently draws Y₁,Y₂,… from Uniform [0,1] until he gets a number larger than X/2, then stops. The expected number of draws that Mr B makes equals (A) 2ln 2 (B) ln 2 (C) 2/e (D) 6/e

Also written as: Ms A selects X from Uniform [0,1]. Mr B repeatedly and independently draws Y_1,Y_2,... from Uniform [0,1] until he gets a number larger than X/2, then stops. The expected number of draws that Mr B makes equals

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

What this question tests

This question is on Geometric and hypergeometric distributions, part of Random variables and standard distributions in Statistics.

Waiting for a first success, and successes in draws without replacement.

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Question from the DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.