## 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: $$-\infty \lt x \lt \infty$$ $$\mu$$ $$\sigma^2$$ $$-\infty \lt \mu \lt \infty$$; $$\sigma \gt 0$$