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Questions › DSE › DSE 2019 › Q40
0 marksStatistics › Random variables and standard distributions › Transformations and order statisticsHardabout 3 min

DSE 2019 Question 40: Random variables and standard distributions

A random number XXX, uniformly distributed on [0,1][0,1][0,1], divides [0,1][0,1][0,1] into 2 segments of lengths XXX and (1−X)(1-X)(1−X). Let RRR be the ratio of the smaller to the larger segment (i.e., R=X/(1−X)R=X/(1-X)R=X/(1−X) or R=(1−X)/XR=(1-X)/XR=(1−X)/X, depending on whether X≤1/2X\le 1/2X≤1/2 or X>1/2X>1/2X>1/2). The distribution of RRR, F(r)F(r)F(r), that is the probability that R≤rR\le rR≤r, equals:

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A random number X, uniformly distributed on [0,1], divides [0,1] into 2 segments of lengths X and (1-X). Let R be the ratio of the smaller to the larger segment (i.e., R=X/(1-X) or R=(1-X)/X, depending on whether X≤ 1/2 or X>1/2). The distribution of R, F(r), that is the probability that R≤ r, equals: (A) 1/(r+1) (B) 2r/(r+1) (C) (1-r)/(1+r) (D) r/(r+1)

Also written as: A random number X, uniformly distributed on [0,1], divides [0,1] into 2 segments of lengths X and (1-X). Let R be the ratio of the smaller to the larger segment (i.e., R=X/(1-X) or R=(1-X)/X, depending on whether X<= 1/2 or X>1/2). The distribution of R, F(r), that is the probability that R<= r, equals:

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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Practise Random variables and standard distributionsMore on Transformations and order statistics

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