For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:

Concept:

Formulas used:

$\mathrm{r}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{C}\mathrm{o}\mathrm{v}\left(\mathrm{x},\mathrm{y}\right)}{\sigma \left(\mathrm{x}\right)\sigma \left(\mathrm{y}\right)}$

Where,

r (x, y) is the Correlation coefficient between x and y

Cov(x, y) Covariance of x and y

σ(x), σ(y) is the standard deviation of x, y respectively

Calculation:

Given:

Correlation coefficient between x and y, r(x, y) = 0.8014

Covariance of x and y, Cov(x, y) = ?

standard deviation y, σ(y) = (25)^1/2 = 5

standard deviation x, σ(x) = (16)^1/2 = 4

We know that, $\mathrm{r}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{C}\mathrm{o}\mathrm{v}\left(\mathrm{x},\mathrm{y}\right)}{\sigma \left(\mathrm{x}\right)\sigma \left(\mathrm{y}\right)}$

$Cov(x,y)=r(x,y)\times \sigma (x)\sigma (y)$

Cov (x, y) = 0.8014 × 5 × 4 = 16.028