Rejection Sampling for Beta distribution

We want to sample from the Beta distribution with the density using Jupyter Python.

$q(x)=\frac{()()}{(+)}{x}^{-1}(1-x{)}^{-1}$

where $(.)$ is the Gamma function and $=2,=2.$

$($a$)$ Aim to use rejection sampling with uniform distribution$(x)=U(x|0,1)$ as the proposal distribution. Compute the corresponding bound $M$ using Jupyter Python.

$($b$)$ Implement the rejection sampling algorithm using the above proposal distribution and bound using Jupyter Python. Check numerically that the expected number of rounds for acceptance is $M.$ Also, check that the histogram of the samples matches the true density.