/Mean-and-Variance

BSD 3-Clause "New" or "Revised" LicenseBSD-3-Clause

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,

image

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

image

Procedure :

  1. Construct frequency distribution for the data

  2. Find the probability distribution from frequency distribution.

  3. Calculate mean using

    image

  4. Find

    image

  5. Calculate variance using

    image

Experiment :

Visual Component

Program :

Developed By : Javith Farkhan S
Reg No : 212221240017

import numpy as np
L=[int (i) for i in input () .split ()]
N=1en (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[il/sf)
mean=p-inner(x,p)
EX2=np-inner (np. square (x), P)
var=EX2-mean**2
SD=np.sqrt(var)
print("The Hean 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 :

Output