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Questions › UoH › UoH 2021 › Q31
1 mark, −0.33Statistics › Joint distributions, covariance and correlation › The correlation coefficientHardabout 2 min

UoH 2021 Question 31: Joint distributions, covariance and correlation

Let V and W be random variables such that the correlation between these two variables is positive but less than 1 (0<Corr(V,W)<10 < \mathrm{Corr}(V,W) < 10<Corr(V,W)<1). Let X=2(V−4)X = 2(V - 4)X=2(V−4) and Y=−0.5W+2Y = -0.5W + 2Y=−0.5W+2. Arrange the following in increasing order of magnitude of correlation:

I. Corr(X,W)\mathrm{Corr}(X,W)Corr(X,W) II. Corr(Y,V)\mathrm{Corr}(Y,V)Corr(Y,V) III. Corr(X,V)\mathrm{Corr}(X,V)Corr(X,V) IV. Corr(Y,W)\mathrm{Corr}(Y,W)Corr(Y,W)

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Let V and W be random variables such that the correlation between these two variables is positive but less than 1 (0 < Corr(V,W) < 1). Let X = 2(V - 4) and Y = -0.5W + 2. Arrange the following in increasing order of magnitude of correlation: I. Corr(X,W) II. Corr(Y,V) III. Corr(X,V) IV. Corr(Y,W) (A) I – II – IV – III (B) II – I – III – IV (C) III – IV – I – II (D) IV – II – I – III

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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