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notation

(NL: notatie)

Sample and population

Sample Population
Size \(n\) \(N\)
Mean \(\overline{x}\) \(\mu\)
Variance \(s^2\) \(\sigma^2\)
Standard deviation \(s\) \(\sigma\)

Probability theory

See also probability

Symbol Interpretation
\(\Omega\) universe
\(A, B, \ldots\) events (with \(A \subset \Omega\), \(B \subset \Omega\), etc.)
\(P(A)\) the probability of event \(A\) (with \(0 \leq P(A) \leq 1\))
\(P(A|B)\) the probability of \(A\) if \(B\) occurs

The normal distribution

If a \(X\) has a normal distribution with expectation value \(\mu\) and standard deviation \(\sigma\), then we write \(X \sim \mathcal{N}(\mu, \ sigma)\).

We write the standard normal distribution as \(Z \sim \mathcal{N}(0, 1)\).

We write the probability distribution of the sample mean as \(M \sim \mathcal{N}(\mu, \frac{\sigma^2}{n})\).

  • \(X \sim \mathcal{N}(\mu, \sigma)\)
    • The stochastic variable \(X\) has a normal distribution with expected value \(\mu\) and standard deviation \(\sigma\)
  • \(Z \sim \mathcal{N}(0, 1)\)
    • The standaad normal distribution.
  • \(M \sim \mathcal{N}(\mu, \frac{\sigma^2}{\sqrt{n}})\)

Statistic hypothesis tests