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Questions › IIT JAM › IIT JAM 2024 › Q35
2 marksStatistics › Joint distributions, covariance and correlation › The correlation coefficientModerateabout 2 min

IIT JAM 2024 Question 35: Joint distributions, covariance and correlation

Let XXX have mean μx\mu_xμx​, variance σx2\sigma_x^2σx2​, and YYY mean μy\mu_yμy​, variance σy2\sigma_y^2σy2​, with correlation ρ\rhoρ. Which of the following is/are CORRECT?

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Answer and worked solution

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Plain-text version

Let X have mean μₓ, variance σₓ², and Y mean μ_y, variance σ_y², with correlation ρ. Which of the following is/are CORRECT? (A) |ρ| ≤ 1 (B) The regression line of Y on X is y = μ_y + ρσₓ/σ_y(x - μₓ) (C) The variance of X - Y is σₓ² + σ_y² - 2ρσₓσ_y (D) ρ = 0 implies X and Y are independent random variables

Also written as: Let X have mean mu_x, variance sigma_x^2, and Y mean mu_y, variance sigma_y^2, with correlation rho. Which of the following is/are CORRECT?

Joint distributions, covariance and correlation has come up 61 times in 7 exams since 2005.

What this question tests

This question is on The correlation coefficient, part of Joint distributions, covariance and correlation in Statistics.

The standardised measure of linear association and what it can and cannot show.

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