5. Discrete random variables

Write a class called Drv (discrete random variable) for the interpretation of finite discrete random variables. The constructor of the class waits for two lists of the same length, the first contains the \(x_k\) values of the random variable \(X\) sorted increasingly, the second contains the probabilities \(p_k=\mathbb{P}(X = x_k)\). Write the following methods:
- __init__: constructor defines two attributes xk and pk for the two lists.
- pdf(x): probability density function of \(X\), returns \(p_k\) if \(x=x_k\), otherwise return 0.
- cdf(x): cumulative distribution function of \(X\), returns \[\sum_{x_k \lt x} p_k.\]
- e(): returns \({\mathbb{E}(X)}\), the expected value of \(X\).
- is_nonneg: this method returns True if the random variable is non-negative, otherwise returns False.
- reweight: this method returns an instant of a random variable \(Y\) from the original \(X\) with the next "reweighting": \[\mathbb{P}(Y=x_k)=\frac{x_kp_k}{\mathbb{E}(X)},\] if \(X\) is non-negative and has at least one nonzero value.
- Binomial: A derived class from Drv for the binomial distribution. Parameters of this class are \(n\) and \(p\). Rewrite the code in this class for the e and for the is_nonneg methods.
- Uniform: A derived class from Drv for the unifor distribution. The parameter of this class is \(n\), the list of values is \([1,2,\dots,n]\). Rewrite the methods mentioned above.
- Geometric: A derived class from Drv for the geometric distribution. The parameter of this class is \(p\). Rewrite the methods signed in the skeleton.py file.

During the writing and testing the code you may try the next or similar interactive sections (the first line shows, how to read and run your code into an interactive section):

>>> exec(open('5YourName.py').read())

>>> y = Drv([25, 33, 40, 50], [1/4]*4 )
>>> y.xk
[25, 33, 40, 50]
>>> y.pk
[0.25, 0.25, 0.25, 0.25]
>>> y
Discrete random variable: (25,0.25) (33,0.25) (40,0.25) (50,0.25) 
>>> y.e()
37.0
>>> x = y.reweight()
>>> x
Discrete random variable: (25,0.16891891891891891) (33,0.22297297297297297) (40,0.2702702702702703) (50,0.33783783783783783) 
>>> x.cdf(42)
0.6621621621621622
>>> x.cdf(52)
1.0

>>> b = Binomial(11, .5)
>>> b.cdf(6)
0.5
>>> b
Binomial random variable: (0,0.00048828125) (1,0.00537109375) (2,0.02685546875) (3,0.08056640625) (4,0.1611328125) (5,0.2255859375) (6,0.2255859375) (7,0.1611328125) (8,0.08056640625) (9,0.02685546875) ...
>>> b.cdf(0)
0
>>> b.cdf(1)
0.00048828125
>>> b.pdf(0)
0.00048828125
>>> br = b.reweight()
>>> br
Discrete random variable: (0,0.0) (1,0.0009765625) (2,0.009765625) (3,0.0439453125) (4,0.1171875) (5,0.205078125) (6,0.24609375) (7,0.205078125) (8,0.1171875) (9,0.0439453125) ...

>>> z = Uniform(3)
>>> z
Uniform random variable: (1,0.3333333333333333) (2,0.3333333333333333) (3,0.3333333333333333) 
>>> z.e()
2.0
>>> z.pdf(2)
0.3333333333333333
>>> z.cdf(3)
0.6666666666666666
>>> z.cdf(4)
1.0

>>> g = Geometric(.1)
>>> g
Geometric random variable: (1,0.1) (2,0.09000000000000001) (3,0.08100000000000002) (4,0.0729) (5,0.06561) (6,0.05904900000000001) (7,0.05314410000000001) (8,0.04782969000000001) (9,0.04304672100000001) (10,0.03874204890000001) ...
>>> g.cdf(3)
0.19
>>> g.cdf(10)
0.6125795110000001
>>> g.cdf(100)
0.9999704873345701
>>> g.is_nonneg()
True
>>> g.e()
10.0
>>> g.reweight()
Traceback (most recent call last):
  File "", line 1, in 
  File "", line 134, in reweight
NotImplementedError: reweight is not implemented for geometric variable!

Please upload the code of the class only and not the code of the usage of it showed above. For helping you we upload a skeleton of the code what you can download also from teams. You may load your code into an interactive section with the next commands.
```
exec(open("5YourName.py").read())
      
```
After this, you may test your code as it is shown above.
Let us practice the PEP 8 recommendations (see python.org, realpython.com,...).
Some help: please recall your knowledge about object oriented programming in Python, you may successfully use list comprehension, for the binomial coefficients you may import the comb function from math package with the command from math import comb .
The purpose of this task is to write a system in object oriented programming style using heritage capable of handling discrete random variables.