Probability

From the observation of a number of events $X_i$ of the same type, we can conclude that such an event may occur with probability

$P(X) = \frac{1}{N}\sum_i X_i$ .

A population of random events can be modeled using the normal distribution:

$X_i = N(\mu, { }\sigma^2)$

The number follows the distribution with mean μ and standard deviation σ (σ² is the variance).

If we have previously derived this distribution for a type of random variable, we can evaluate the fit of every next instance of the variable to the distribution:

$Z_i = \frac{X_i - \mu}{\sigma^2}$

The Z-value measures how many standard deviations the value X_i deviates from the mean. The larger the Z-value the less likely does the value X_i follow this normal distribution, thus $X_i \sim N(\mu, { }\sigma^2)$ .

TODO: include calculator.