Estimate correlation and co variance.

Solutions:

$\overline{X_1} = 6.14$

$\overline{X_2} = 101.8$

$\overline{X_1 X_2} = 625.052$

$\sum^2_1 x_1 x_2 = 6328.5$

$\sigma^2_2 = \frac{\sum^n_1 x^2_1 – n x^2_1}{n-1} = \frac{386.44 – 10 \times (6.14)^2}{9}$

$\sigma^2_2 = \frac{\sum^n_1 x^2_1 – n x^2_1}{n-1} = \frac{104520 – 10 \times (101.8)^2}{9}$

$= 98.62$

$\therefore$ $\sigma_1 = 1.02$ and $\sigma_2 = 9.93$

$co^v (x_1 x_2) = \frac{1}{1-n} /sum^n_1 x_1 x_2 – \bar{X_1 X_2}$

$= \frac{6328.5 – 6250.52}{10-1} = 8.66$

Corelation $\rho = \frac{ cov (x_1 x_2)}{ \sigma_1 \sigma_2}$

$= \frac{8.66}{(1.02) (9.93)} = 0.86$