Question

Calculate the Pearsons correlation coefficient

Answer 1

Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. 

$$\rho (X, Y) = \frac{cov(X, Y)} {\sigma(X) ×\sigma(Y) } ,$$ $$\sigma(X) = \sqrt{E[(X - E[X])^2]} ,$$

$$\sigma(Y) = \sqrt{E[(Y - E[Y])^2]} ,$$ $$cov (X, Y) = E[XY] - E[X]×E[Y],$$

where E is mean.