5.6 Summary

Table 5.1 summarises some important distributions.

TABLE 5.1: Summary of common 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: $-\infty \lt x \lt \infty$	$\mu$	$\sigma^2$	$-\infty \lt \mu \lt \infty$ ; $\sigma \gt 0$