# 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 $f(x)={\frac {1}{\sqrt {2\pi \sigma }}}e^{-(x-\mu )^{2}/2\sigma ^{2}},-\infty 0$ 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 Example
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