Use python with root library:https://root.cern

Question 2 Central limit theorem

The random variable x follows a pdf f(x). Consider four choices of f(x):

a) Uniform distribution between 0 and 11

b) Uniform distribution between 0.4 and 0.6

c) Poisson distribution with mean of 1

d) Exponential distribution with mean of 1.

For each of these pdfs, define a canvas and draw histograms each with 10000 entries sampled from the following observables:

1. x

2. Σ 1 1/2

3. i 1 ₁/5

4. Σ1 π./100.

This will give 16 different histograms, 4 on each figure [using one canvas for each pdf defined in (a)-(d) above]. Normalize the histograms such that they approximate the associated pdf. On each of these plots, also draw a Gaussian pdf (as a function) with mean and variance consistent with the expectation from the central limit theorem.