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Questions › DSE › DSE 2014 › Q43
2 marks, −0.666666666666667Statistics › Random variables and standard distributions › Expectation and varianceHardabout 3 min

DSE 2014 Question 43: 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 sum of the numbers Mr B draws, given X=xX=xX=x, 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 sum of the numbers Mr B draws, given X=x, equals (A) ln 2 (B) 1/(1-1/2) (C) 1/(2-x) (D) 3/(1-1/2)

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 sum of the numbers Mr B draws, given X=x, equals

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

What this question tests

This question is on Expectation and variance, part of Random variables and standard distributions in Statistics.

The mean and spread of a random variable, and how they change under transformations and sums.

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