Problem #$3$

Write a Python function named CentralLimitDemoPoisson that takes as input arguments:

$n-$ the number of samples to be taken from an exponential distribution,

sample$\_$sizes $-$ a $16$ numpy array holding the size of each of the $n$ samples for that value of $n$ different size of each sample for a fixed,

mu $-$ the mean $($and variance$)$ of the Poisson random variable.

And returns as output:

fig $-$ a figure displaying six histograms, one for each value of sample$\_$size specified for the given value of $n,$

sample$\_$means $-$ a numpy array of size $1x$ holding the $n$ sample$\_$means,

sample$\_$means$\_$stdevs $-$ a numpy array of size $16$ holding the standard deviation of the list of sample$\_$means.

Test your function by setting sample$\_$sizes $=np.$ array $([4,50,100,500,1000,2000])$ and running the command fig$7,$ means $7,$ devs $7=$

CentralimitDemoPoisson$(1000,$ sample$\_$sizes, $100).$