# 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 ${\displaystyle \mu =\sum {xp(x)}}$  Example
4.2.2 Variance of a frequency distribution ${\displaystyle \sigma ^{2}=\sum {(x-\mu )^{2}p(x)}}$

or ${\displaystyle \sigma ^{2}=\sum {x^{2}p(x)-\mu ^{2}}}$

Example
4.3.1 Combination of objects ${\displaystyle {}_{n}C_{k}={\frac {n!}{x!(n-1)!}}}$  Example
4.3.2 Binomial distribution function ${\displaystyle f(x)={}_{n}C_{k}p^{x}q^{n-x},x=0,1,2,...}$  Example
4.3.3–4.3.5 Tabled binomial probability equalities ${\displaystyle P(X=x|n,p\geq .50)=P(X=n-x|n,1-p)}$

${\displaystyle P(X\leq x|n,p>.50)=P(X\geq n-x|n,1-p)}$  ${\displaystyle P(X\geq x|n,p>.50)=P(X\leq n-x|n,1-p)}$

Example
4.4.1 Poisson distribution function ${\displaystyle f(x)={\frac {e^{-\lambda }\lambda ^{x}}{x!}},x=0,1,2,\dots }$  Example
4.6.1 Normal distribution function ${\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma }}}e^{-(x-\mu )^{2}/2\sigma ^{2}},-\infty 0}$  Example
4.6.2 z-transformation ${\displaystyle z={\frac {X-\mu }{\sigma }}}$  Example
4.6.3 Standard normal distribution function ${\displaystyle f(z)={\frac {1}{\sqrt {2\pi }}}e^{-z^{2}/2},-\infty   Example
Symbol Key