Biostatistics with R/Probability Distributions

Summary of Formulars with R

Formular Number	Name	Formular	Formular with R
4.2.1	Mean of a frequency distribution	$\mu =\sum {xp(x)}$	Example
4.2.2	Variance of a frequency distribution	$\sigma ^{2}=\sum {(x-\mu )^{2}p(x)}$ or $\sigma ^{2}=\sum {x^{2}p(x)-\mu ^{2}}$	Example
4.3.1	Combination of objects	${}_{n}C_{k}={\frac {n!}{x!(n-1)!}}$	Example
4.3.2	Binomial distribution function	$f(x)={}_{n}C_{k}p^{x}q^{n-x},x=0,1,2,...$	Example
4.3.3–4.3.5	Tabled binomial probability equalities	$P(X=x\|n,p\geq .50)=P(X=n-x\|n,1-p)$ $P(X\leq x\|n,p>.50)=P(X\geq n-x\|n,1-p)$ $P(X\geq x\|n,p>.50)=P(X\leq n-x\|n,1-p)$	Example
4.4.1	Poisson distribution function	$f(x)={\frac {e^{-\lambda }\lambda ^{x}}{x!}},x=0,1,2,\dots$	Example
4.6.1	Normal distribution function	$f(x)={\frac {1}{\sqrt {2\pi \sigma }}}e^{-(x-\mu )^{2}/2\sigma ^{2}},-\infty <x<\infty ,-\infty <\mu <\infty ,\sigma >0$	Example
4.6.2	z-transformation	$z={\frac {X-\mu }{\sigma }}$	Example
4.6.3	Standard normal distribution function	$f(z)={\frac {1}{\sqrt {2\pi }}}e^{-z^{2}/2},-\infty <z<\infty$	Example
Symbol Key