Distribuzioni

08/07/202426/12/2018 di admin

	…	Media	Varianza	F. densità di probabilità	F. di distribuzione
Binomiale	…	$np$	$npq$	f(k) = ${n \choose k}\ p^k\ q^{n-k}$	…
Di Poisson	…	$\lambda$	$\lambda$	f(k) = $e^{-\lambda}\ \frac{\lambda^k}{k!}$	…
Geometrica	…	$\displaystyle \frac{1}{p}$	$\displaystyle \frac{q}{p^2}$	f(k) = $pq^{k-1}$	F(k) = $1-q^k$
Normale	…	μ	σ²	f(x) = $\frac{1}{\sigma \sqrt{2\pi}}\ e^{\frac{-(x-\mu)^2}{2\sigma^2}}$	F(x) = $\displaystyle \frac{1}{\sigma \sqrt{2\pi}}\ \int_{-\infty}^x \ e^{\frac{-(x-\mu)^2}{2\sigma^2}} \ dx$
Normale standardizzata	…	0	1	f(z) = $\displaystyle \frac{1}{\sqrt{2\pi}}\ \ e^{\frac{-z^2}{2}}$	F(z) = $\displaystyle \frac{1}{\sqrt{2\pi}}\ \int_{-\infty}^z \ e^{\frac{-z^2}{2}} \ dz$
Esponenziale	…	$\displaystyle \frac{1}{\lambda}$	$\displaystyle \frac{1}{\lambda^2}$	f(x) = $\lambda e^{-\lambda x}$	F(x) = $1-e^{-\lambda x}$
Uniforme	…	$\displaystyle \frac{1}{2}(a+b)$	$\displaystyle \frac{1}{12}(b-a)^2$	f(x) = $<p class=$ $\begin{cases} \frac{1}{b-a} & \text{se $x\in [a,\ b]$} \\ \\ \\ 0 & \text{se $x\notin [a,\ b]$} \end{cases}$ ” align=”absmiddle”>	F(x) = $<p class=$ $\begin{cases} 0 & \text{se $x\in (-\infty,\ a)$} \\ \\ \\ \frac{x-a}{b-a} & \text{se $x\in [a,\ b)$} \\ \\ \\ 1 & \text{se $x\in [b, \ +\infty]$} \end{cases}$ ” align=”absmiddle”>