An Introduction to Probability and Statistical Inference, 2nd Edition

Table 7

Table of Selected Discrete and Continuous Distributions and Some of Their Characteristics

Probability Density Functions in One Variable
Distribution	Probability Density Function	Mean	Variance
Binomial, B(n, p)	$\begin{array}{l}f\left(x\right)=\left(\begin{array}{c}n\\ x\end{array}\right)p^x{q}^{n-x},x=0,1,\dots ,n;\\ 0<p<1,q=1-p\end{array}$	np	npq
Bernoulli, B(1, p)	$f\left(X\right)=p^x{q}^{1-x},x=0,1$	p	pq
Geometric	$\begin{array}{l}f\left(X\right)=p{q}^{x-1},x=1,2,\dots ;\\ 0<p<1,q=1-p\end{array}$	$\frac{1}{p}$	$\frac{q}{p^2}$
Poisson, P(λ) ...