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Questions › DSE › DSE 2021 › Q45
4 marks, −1Statistics › Joint distributions, covariance and correlation › Covariance and its propertiesModerateabout 2 min

DSE 2021 Question 45: Joint distributions, covariance and correlation

Let X1,X2X_1, X_2X1​,X2​ and X3X_3X3​ be three (pairwise) uncorrelated random variables. The mean and variance of each variable is 0 and 3, respectively. Find the correlation between (X1+X2)(X_1 + X_2)(X1​+X2​) and (X1+X3)(X_1 + X_3)(X1​+X3​).

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Let X₁, X₂ and X₃ be three (pairwise) uncorrelated random variables. The mean and variance of each variable is 0 and 3, respectively. Find the correlation between (X₁ + X₂) and (X₁ + X₃). (A) 0 (B) 1/2 (C) 1/3 (D) 1

Also written as: Let X_1, X_2 and X_3 be three (pairwise) uncorrelated random variables. The mean and variance of each variable is 0 and 3, respectively. Find the correlation between (X_1 + X_2) and (X_1 + X_3).

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

What this question tests

This question is on Covariance and its properties, part of Joint distributions, covariance and correlation in Statistics.

How two variables move together and how covariance combines.

TestStop has 9 past-paper questions on this subtopic.

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Question from the DSE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.