I need a python script.

Exercise $3$: Random sample generator

Write a Python script that generates random numbers distributed according to a Breit$-$

Wigner distribution with the statistical median $m=3$ and the full$-$width at half maximum

$b=7.$ Use for the PDF and CDF the following expressions:

$p(x)=\frac{1}{}\frac{b}{(x-m{)}^2+b^2},$

$F(a)=\frac{1}{2}+\frac{1}{}arctan(\frac{a-m}{b}).$

Generate $N_{smpl}=10000$ accepted values of $x,$ distributed according to $p(x)$ using the following

methods discussed in the lecture:

$($a$)$ Accept$-$reject method.

$($b$)$ Inverting the CDF$.$

For each of the two methods, plot the histogram of the generated sample and superimpose

the PDF after normalising it to match the histogram.