AttackOfTheSam

Expected Value

First moment

$$\bar{X} = E[ X ] = \int_{-\infty}^{\infty}{x f(x) dx}$$

Second moment

$$\bar{X^2} = E[ X^2 ] = \int_{-\infty}^{\infty}{x^2 f(x) dx}$$

Nth Moment

$$\bar{X^n} = E[ X^n ] = \int_{-\infty}^{\infty}{x^n f(x) dx}$$

Variance

$$\sigma^2 = \overline{(X-\bar{X})^2} = E[(X-\overline{X})^2] = \int_{-\infty}^{\infty}{(x-\bar{X})^2 f(x) dx}$$

Autocorrelation

$$R_x(t_1,t_2) = E[X_1 X_2] = \int_{-\infty}^{\infty} dx_1 \int_{-\infty}^{\infty}{x_1 x_2 f(x_1,x_2) d x_2} $$

Sam Uncategorized