Question

If the variances of two variables x and y are respectively 9 and 16 and their covariance is 8, then their coefficient of correlation is

• A. $\frac{2}{3}$
• B. $\frac{8}{3\sqrt{2}}$
• C. $\frac{9}{8\sqrt{2}}$
• D. $\frac{2}{9}$

Answer 1

Answer: (A)

$\frac{2}{3}$

Answer 2

Coefficient of correlation

$r = \frac{C ⥂ ov(x,y)}{\sqrt{Var(x)}.\sqrt{Var(y)}}$ = $\frac{8}{\sqrt{9}\sqrt{16}} \Rightarrow r = \frac{2}{3}$.