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
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

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.