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	$P(X=x|n,p\ge .50)=P(X=n-x|n,1-p)$ $P(X\le x|n,p>.50)=P(X\ge n-x|n,1-p)$ $P(X\ge x|n,p>.50)=P(X\le n-x|n,1-p)$	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	$f(x)=\frac{1}{\sqrt{2\pi \sigma }}{e}^{-(x-\mu {)}^2/2{\sigma }^2},-\mathrm{\infty }<x<\mathrm{\infty },-\mathrm{\infty }<\mu <\mathrm{\infty },\sigma >0$	Example
4.6.2	z-transformation	$z=\frac{X-\mu }{\sigma }$	Example
4.6.3	Standard normal distribution function	$f(z)=\frac{1}{\sqrt{2\pi }}{e}^{-z^2/2},-\mathrm{\infty }<z<\mathrm{\infty }$	Example
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