23008112 / Mean-and-Variance

Mean and variance of a discrete distribution

Aim :

To find mean and variance of arrival of objects from the feeder using probability distribution

Software required :

Python and Visual components tool

Theory:

The expectation or the mean of a discrete random variable is a weighted average of all possible values of the random variable. The weights are the probabilities associated with the corresponding values. It is calculated as,

The variance of a random variable shows the variability or the scatterings of the random variables. It shows the distance of a random variable from its mean. It is calcualted as

Procedure :

1. Construct frequency distribution for the data

2. Find the probability distribution from frequency distribution.

3. Calculate mean using

   

4. Find

   

5. Calculate variance using

   

Experiment :

Program :

Name:  R. Sanjana
Department: Artificial Intelligence and Machine Learning
Reg.No: 212223240148

import numpy as np
L=[int(i) for i in input().split()]
N=len(L);M=max(L)
X=list();f=list()
for i in range(M+1):
    c=0
    for j in range(N):
        if L[j]==i:
            c=c+1
    f.append(c)
    X.append(i)
sf=np.sum(f)
p=list()
for i in range(M+1):
    p.append(f[i]/sf)
mean=np.inner(X,p)
EX2=np.inner(np.square(X),p)
var=EX2-mean**2
SD=np.sqrt(var)
print("The mean arrival rate is %.3f"%mean)
print("The variance of arrival from feeder is %.3f"%var)
print("The standard deviation of arrival deom feeder is %.3f"%SD)

Output :

Results :

The mean and variance of arrivals of objects from feeder using probability distribution are calculated.