value, expected

(NL: waarde, verwachte)

The expected value of a stochastic variable is the average of all values the variable can take, weighted by the probability that value occurs.

For a discrete stochastic variable, we denote the expected value as \(\mu_X\) or \(E(X)\) and calculate it as follows:

\[\mu_x = \sum_{i=1}^{n} x_i \cdot P(X = x_i)\]

with \(\Omega = {x_1, \ldots, x_n}\) the sample space of \(X\).

For a continuous stochastic variable, you get:

\[\mu_x = \int_{-\infty}^{+\infty} x \cdot f(x) \, \mathrm{d}x\]

where \(f(x)\) is the probability density function.

You can also calculate the variance and standard deviation of a stochastic variable.