- Muchas notas - Fran Acién

$E(X) = \mu = \text{Expected Value} = \sum_i x_i p_x(X = x_i)$

The expected value is the probabilistic mean.

$Var(X) = \sigma^2 = \text{Variance} = E[X^2] - E^2[X]$ The variance measure the dispersion.

Standard deviation is:

$\sigma_X = \text{standard deviation} = \sqrt{Var(X)}$ The correlation means the dependency between two random variables. The normaliced correlation is defined as:

$\rho_{X,Y} = corr(X, Y) = \frac{cov(X, Y)}{\sigma_X \sigma_Y} = \frac{E[(X - \mu_X )]E[(Y - \mu_Y )]}{\sigma_X \sigma_Y}$ Where cov means covariance.

The autocorrelation means the correlation between one random variable and a delayed copy of it.

Gaussian distribution:

$f(X) = \frac{1}{\sigma \sqrt{2 \pi}} \exp {-\frac{(x - \mu)^2}{2 \sigma^2}}$

20221130 - Fast concepts of Probability theory

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