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Questions › DSE › DSE 2017 › Q39
2 marks, −0.666666666666667Statistics › Random variables and standard distributions › The normal distributionModerateabout 3 min

DSE 2017 Question 39: Random variables and standard distributions

Let XXX and YYY be independent standard Normal random variables, and let P(X>1)=pP(X>1)=pP(X>1)=p. The probability of the event {X2>1 and Y3<1}\{X^2>1 \text{ and } Y^3<1\}{X2>1 and Y3<1} is

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Let X and Y be independent standard Normal random variables, and let P(X>1)=p. The probability of the event {X²>1 and Y³<1} is (A) 2p(1-p) (B) 4p (C) p(1-p) (D) 2p²

Also written as: Let X and Y be independent standard Normal random variables, and let P(X>1)=p. The probability of the event {X^2>1 and Y^3<1} is

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

What this question tests

This question is on The normal distribution, part of Random variables and standard distributions in Statistics.

The bell curve: standardising, tail probabilities and approximations.

TestStop has 20 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q57Let X₁, X₂, X₃, X₄ be independent standard normal variables and Y = (X₁ + X₂)² + (X₃ + X₄)². The variance of…
  • IIT JAM 2022 · Q31Let X ~ N(μ_X, σ_X²) and Y ~ N(μ_Y, σ_Y²). Which of the following is/are NOT correct?
Practise Random variables and standard distributionsMore on The normal distribution

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Question from the DSE 2017 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.