rithishv / 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 :

DEVELOPED BY : RITHISH V

REGISTER NO:2122232401140

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 from feeder is %.3F "%SD)

Output :

Results :

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