Let X and Y be two random variables with , , , , and . Find (i) Cov[X,Y]; (ii) the Pearson correlation coefficient ; (iii) .
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2 marksStatisticsJoint distributions, covariance and correlationCovariance and its propertiesModerateabout 3 min
DSE 2007 Question 57: Joint distributions, covariance and correlation
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Let X and Y be two random variables with E[X]=3, E[Y]=0, V[X]=4, V[Y]=25, and E[XY]=5. Find (i) Cov[X,Y]; (ii) the Pearson correlation coefficient ρ_(X,Y); (iii) V[X+Y]. (A) 0.5, 5, 39 (B) 5, 0.5, 34 (C) 5, 5, 39 (D) 5, 0.5, 39
Also written as: Let X and Y be two random variables with E[X]=3, E[Y]=0, V[X]=4, V[Y]=25, and E[XY]=5. Find (i) Cov[X,Y]; (ii) the Pearson correlation coefficient rho_(X,Y); (iii) V[X+Y].
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 2007 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.