Question

If variables X takes values $x_1,x_2,x_3....$ and Y takes values $y_1,y_2,y_3....$, then covariance between X and Y is defined as

• A. $\frac{1}{n}\sum (x-\overline{x})(y-\overline{y})$
• B. $\frac{1}{n}\sum (x^2-\overline{x})(y^2-\overline{y})$
• C. $\frac{1}{n}\sum (x-{\overline{x}}^2)(y-{\overline{y}}^2)$
• D. $\sum (x-\overline{x})(y-\overline{y})$

Answer 1

Answer: (A)

$\frac{1}{n}\sum (x-\overline{x})(y-\overline{y})$

If variables $X$ takes values $x_1,x_2,x_3....$ and $Y$ takes values $y_1,y_2,y_3....,$ then covariance between $X$ and $Y$ is defined as

$\frac{1}{n}\sum (x-\overline{x})(y-\overline{y})$

Where,

$x-$ The values of the $X-$variable

$y-$ The values of the $Y-$variable

$\overline{x}-$ The mean (average) of the $X-$variable

$\overline{y}-$ The mean (average) of the $Y-$ variable

$n-$ The number of the data points