An Introduction to Probability and Statistical Inference, 2nd Edition

Inside Front Matter

Probability Density Functions in One Variable
Distribution	Probability Density Function	Mean	Variance
Binomial, B(n, p)	$\begin{array}{l}f\left(x\right)=\left(\begin{array}{c}n\\ x\end{array}\right)p^x{q}^{n-x},x=0,1,\dots ,n;\\ 0<p<,q=1-p\end{array}$	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)	$f\left(x\right)=e^{-\lambda }\frac{{\lambda }^x}{X!},X=0,1,\dots ;\lambda >0$	λ	λ
Hypergeometric	$\begin{array}{l}f\left(x\right)=\frac{\left(\begin{array}{c}m\\ x\end{array}\right)\left(\begin{array}{c}n\\ r-X\end{array}\right)}{\left(\begin{array}{c}m+n\\ r\end{array}\right)},\text{where}\\ X=0,\text{1,}\dots \text{,}r\end{array}$