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Questions › IIT JAM › IIT JAM 2024 › Q12
2 marks, −0.667Statistics › Random variables and standard distributions › The normal distributionEasyabout 1 min

IIT JAM 2024 Question 12: Random variables and standard distributions

Consider two independent random variables: X∼N(5,4)X \sim N(5, 4)X∼N(5,4) and Y∼N(3,2)Y \sim N(3, 2)Y∼N(3,2). If (2X+3Y)∼N(μ,σ2)(2X + 3Y) \sim N(\mu, \sigma^2)(2X+3Y)∼N(μ,σ2), then the values of mean (μ\muμ) and variance (σ2\sigma^2σ2) are

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Consider two independent random variables: X ~ N(5, 4) and Y ~ N(3, 2). If (2X + 3Y) ~ N(μ, σ²), then the values of mean (μ) and variance (σ²) are (A) μ = 19 and σ² = 34 (B) μ = 8 and σ² = 14 (C) μ = 19 and σ² = 14 (D) μ = 8 and σ² = 34

Also written as: Consider two independent random variables: X ~ N(5, 4) and Y ~ N(3, 2). If (2X + 3Y) ~ N(mu, sigma^2), then the values of mean (mu) and variance (sigma^2) are

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