• $\begin{array}{l}x=\left[1,3,7,5\right]\\ \max \left(x\right)\\ \mathrm{>>>}7\end{array}$

• $\begin{array}{l}x=\left[1,3,7,5\right]\\ \min \left(x\right)\\ \mathrm{>>>}1\end{array}$

• $\begin{array}{l}x=\left[1,3,7,5\right]\\ \mathrm{sort}\left(x\right)\\ \mathrm{>>>}=\left[1,3,5,7\right]\end{array}$

• $\begin{array}{l}x=\left[1,3,7,5\right]\\ \mathrm{mean}\left(x\right)\\ \mathrm{>>>}4.0\end{array}$

• $\begin{array}{l}x=\left[1,3,7,5\right]\\ \mathrm{var}\left(x\right)\\ \mathrm{>>>}5.0\end{array}$

• $\begin{array}{l}x=\left[1,3,7,5\right]\\ \mathrm{std}\left(x\right)\\ \mathrm{>>>}2.2360679775\end{array}$

• $\begin{array}{l}x=\mathrm{Die}\left(6\right)\\ \mathrm{>>>}x=\mathrm{Die}\left(6\right)\\ P\left\{\mathrm{x>=4}\right\}\\ \mathrm{>>>}0.5\\ E\left(x\right)\\ \mathrm{>>>}3.5\\ D\left(x\right)\\ \mathrm{>>>}2.91666666666667\\ \sigma \left(x\right)\\ \mathrm{>>>}1.70782512765993\\ \mathrm{pdf}\left(x\right)\\ \mathrm{>>>}\{1:\frac{1}{6},2:\frac{1}{6},3:\frac{1}{6},4:\frac{1}{6},5:\frac{1}{6},6:\frac{1}{6}\}\end{array}$

The density of the Binomial distribution is given by:

$\begin{array}{l}P\{X=k\}=\left(\begin{array}{l}n\\ k\end{array}\right)p^k{\left(\mathrm{1-p}\right)}^{\mathrm{n-k}}k=\mathrm{0,1,2,...,n}\end{array}$

• $\begin{array}{l}x=b(4,0.5)\\ \mathrm{>>>}x=b(4,0.5)\\ P\left\{\mathrm{x>=4}\right\}\\ \mathrm{>>>}0.0625\\ E\left(x\right)\\ \mathrm{>>>}2\\ D\left(x\right)\\ \mathrm{>>>}1\\ \sigma \left(x\right)\\ \mathrm{>>>}1\\ \mathrm{pdf}\left(x\right)\\ \mathrm{>>>}\{0:0.0625,1:0.25,2:0.375,3:0.25,4:0.0625\}\end{array}$

The density of the Poisson distribution is given by:

$\begin{array}{l}P\{X=k\}=\frac{{\lambda }^k{e}^{\mathrm{-\lambda }}}{\mathrm{k!}}\end{array}$

• $\begin{array}{l}x=\pi \left(3\right)\\ \mathrm{>>>}x=\pi \left(3\right)\\ E\left(x\right)\\ \mathrm{>>>}3\\ D\left(x\right)\\ \mathrm{>>>}3\\ \sigma \left(x\right)\\ \mathrm{>>>}1.73205080756888\\ \mathrm{pdf}\left(x\right)\\ \mathrm{>>>}\frac{3^k}{e^3\mathrm{*(k)!}}\end{array}$

The density of the Uniform distribution is given by:

$\begin{array}{l}f(x)=\left\{\begin{array}{l}\frac{1}{\mathrm{b-a}}\mathrm{x\in [a,b]}\\ 0\mathrm{otherwise}\end{array}\right.\end{array}$

• $\begin{array}{l}x=U(1,7)\\ \mathrm{>>>}x=U(1,7)\\ P\left\{\mathrm{x>3}\right\}\\ \mathrm{>>>}0.666666666666667\\ E\left(x\right)\\ \mathrm{>>>}4\\ D\left(x\right)\\ \mathrm{>>>}3\\ \sigma \left(x\right)\\ \mathrm{>>>}1.73205080756888\\ \mathrm{pdf}\left(x\right)\\ \mathrm{>>>}\frac{1}{6}\end{array}$

The density of the Exponential distribution is given by:

$\begin{array}{l}f(x)=\left\{\begin{array}{l}\frac{1}{\theta }{e}^{\mathrm{-x/\theta }}\mathrm{x>0}\\ 0\mathrm{otherwise}\end{array}\right.\end{array}$

• $\begin{array}{l}x=\mathrm{Expd}\left(10\right)\\ \mathrm{>>>}x=\mathrm{Expd}\left(10\right)\\ P\left\{\mathrm{x>3}\right\}\\ \mathrm{>>>}9.35762296884017e-14\\ E\left(x\right)\\ \mathrm{>>>}0.1\\ D\left(x\right)\\ \mathrm{>>>}0.01\\ \sigma \left(x\right)\\ \mathrm{>>>}0.1\\ \mathrm{pdf}\left(x\right)\\ \mathrm{>>>}10*e^{\mathrm{-10}*x}\end{array}$

The density of the Normal distribution is given by:

$\begin{array}{l}f(x)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{{\left(\mathrm{x-\mu }\right)}^2}{2{\sigma }^2}}\end{array}$

• $\begin{array}{l}x=N(0,1)\\ \mathrm{>>>}x=N(0,1)\\ P\left\{\mathrm{x>3}\right\}\\ \mathrm{>>>}0.00134989803163009\\ E\left(x\right)\\ \mathrm{>>>}0\\ D\left(x\right)\\ \mathrm{>>>}1\\ \sigma \left(x\right)\\ \mathrm{>>>}1\\ \mathrm{pdf}\left(x\right)\\ \mathrm{>>>}\frac{\sqrt{2}}{2*\sqrt{\pi }}*e^{-\frac{x^2}{2}}\end{array}$

The density of the Chi-squared distribution is given by:

$\begin{array}{l}f(x)=\left\{\begin{array}{l}\frac{1}{2^{\mathrm{n/2}}\Gamma \left(\mathrm{n/2}\right)}{x}^{\mathrm{n/2-1}}{e}^{\mathrm{-x/2}}\mathrm{x>0}\\ 0\mathrm{otherwise}\end{array}\right.\end{array}$

• $\begin{array}{l}x={\chi }^2\left(6\right)\\ \mathrm{>>>}x={\chi }^2\left(6\right)\\ P\left\{\mathrm{x>3}\right\}\\ \mathrm{>>>}0.808846830538058\\ E\left(x\right)\\ \mathrm{>>>}6\\ D\left(x\right)\\ \mathrm{>>>}12\\ \sigma \left(x\right)\\ \mathrm{>>>}3.46410161513775\\ \mathrm{pdf}\left(x\right)\\ \mathrm{>>>}\frac{x^2}{16}*e^{-\frac{x}{2}}\end{array}$

The density of the t distribution is given by:

$\begin{array}{l}f(x)=\frac{\Gamma \left(\mathrm{(n+1)/2}\right)}{\sqrt{\mathrm{\pi n}}\Gamma \left(\mathrm{n/2}\right)}{\left(\mathrm{1+}\frac{x^2}{n}\right)}^{\mathrm{-(n+1)/2}}\end{array}$

• $\begin{array}{l}x=t\left(6\right)\\ \mathrm{>>>}x=t\left(6\right)\\ P\left\{\mathrm{x>3}\right\}\\ \mathrm{>>>}0.0120040983778655\\ E\left(x\right)\\ \mathrm{>>>}0\\ D\left(x\right)\\ \mathrm{>>>}1.5\\ \sigma \left(x\right)\\ \mathrm{>>>}1.22474487139159\end{array}$

The density of the F distribution is given by:

$\begin{array}{l}f(x)=\left\{\begin{array}{l}\frac{\Gamma \left(\mathrm{(m+n)/2}\right){\mathrm{(m/n)}}^{\mathrm{m/2}}{x}^{\mathrm{(m/2)-1}}}{\Gamma \left(\mathrm{m/2}\right)\Gamma \left(\mathrm{n/2}\right){\mathrm{(1+(mx/n))}}^{\mathrm{(m+n)/2}}}\mathrm{x>0}\\ 0\mathrm{otherwise}\end{array}\right.\end{array}$

• $\begin{array}{l}x=F(2,6)\\ \mathrm{>>>}x=F(2,6)\\ P\left\{\mathrm{x>3}\right\}\\ \mathrm{>>>}0.125\\ E\left(x\right)\\ \mathrm{>>>}1.5\\ D\left(x\right)\\ \mathrm{>>>}6.75\\ \sigma \left(x\right)\\ \mathrm{>>>}2.59807621135332\end{array}$