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Questions › DSE › DSE 2016 › Q34
0 marksStatistics › Random variables and standard distributions › Expectation and varianceHardabout 3 min

DSE 2016 Question 34: Random variables and standard distributions

Suppose XXX has a normal distribution with mean 0 and variance σ2\sigma^2σ2. Let YYY be an independent random variable taking values −1-1−1 and 111 with equal probability. Define Z=XY+XYZ=XY+\dfrac{X}{Y}Z=XY+YX​. Which of the following is true?

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Plain-text version

Suppose X has a normal distribution with mean 0 and variance σ². Let Y be an independent random variable taking values -1 and 1 with equal probability. Define Z=XY+X/Y. Which of the following is true? (A) Var(Z)>σ² (B) Var(Z)<σ² (C) Var(Z)=σ² (D) Var(Z) can be greater than or smaller than σ²

Also written as: Suppose X has a normal distribution with mean 0 and variance sigma^2. Let Y be an independent random variable taking values -1 and 1 with equal probability. Define Z=XY+X/Y. Which of the following is true?

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 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.