5.6 Summary
Table 5.1 summarises some important distributions.
| Reference | Type | Mean | Variance | Notes | |
|---|---|---|---|---|---|
| Poisson | Sect. 5.1 | Discrete: \(x = 0, 1, 2, \dots\) | \(\mu\) | \(\mu\) | \(\mu \gt 0\) |
| Binomial | Sect. 5.2 | Discrete: \(x = 0, 1, \dots, n\) | \(np\) | \(np(1-p)\) | \(0 \lt p \lt 1\) and \(n \ge 1\) an integer |
| Geometric | Sect. 5.3 | Discrete: \(x = 0, 1, 2, \dots\) | \(\displaystyle\frac{1}{p}\) | \(\displaystyle\frac{1-p}{p^2}\) | \(0 \lt p \lt 1\) |
| Exponential | Sect. 5.4 | Continuous: \(x\gt 0\) | \(\mu\) | \(\mu^2\) | \(\mu\gt0\) |
| Normal | Sect. 5.5 | Continuous: \(-\infty \lt x \lt \infty\) | \(\mu\) | \(\sigma^2\) | \(-\infty \lt \mu \lt \infty\); \(\sigma \gt 0\) |