Question

Find the correlation coefficient between the tandom variables X and Y if the covariance of X and Y is 0.9 and variances of the random variables X and Y are 4 and 9, respectively 1)0.142 2)0.133 3)0.150 4)0.125

Random variables
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asked 2021-06-04
Find the correlation coefficient between the tandom variables X and Y if the covariance of X and Y is 0.9 and variances of the random variables X and Y are 4 and 9, respectively
1)0.142
2)0.133
3)0.150
4)0.125

Answers (1)

2021-06-05

Step 1
Given: \(Cov(X, Y) = 0.9\)
\(Var(X) = 4\ \&\ Var(Y) = 9\)
The coefficient of correlation is given by
\(r=\frac{Cov(X,Y)}{\sqrt{Var(X)Var(Y)}}\)
\(=\frac{0.9}{\sqrt{4\times 9}}\)
\(=0.15\)
Step 2
Hence the correlation between \(X\ \&\ Y\) is 0.150.

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