Pearson’s Correlation Coefficient is defined as follows:
$$ =\frac{\left(,\right)}{_x_y}=\frac{\left[\left(−_x\right)\left(−_y\right)\right]}{\sqrt{E\left(\left[\left(−_x\right)^2\right]\right)}\sqrt{E\left(\left[\left(y−_y\right)^2\right]\right)}} $$
how can I show that −1≤≤1 using Cauchy–Schwarz inequality ? Can anyone maybe give a link to a good explanation or a book with a detailed proof which uses Cauchy–Schwarz inequality ?
