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# Binomial Process | Linear Algebra using Python

**Linear Algebra using Python | Binomial Process**: Here, we are going to learn about the binomial process and its implementation in Python.

Submitted by Anuj Singh, on June 13, 2020

When we flip a coin, there are two possible outcomes as head or tail. Each outcome has a fixed probability of occurrence. In the case of fair coins, heads and tails each have the same probability of 1/2. In addition, there are cases in which the coin is biased, so that heads and tails have different probabilities of occurrence. Coin toss experiment for number of n trails can be called as a *binomial distribution*.

As per Wikipedia Definition: *In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.*

Here, we will learn to create a binomial distribution using python with Probability parameter **p = 0.1**.

## Python code for Binomial Process

# Linear Algebra Learning Sequence # Binomial Process import pylab as pl # defining factorial function k = 0 def fact(num): facto = 1 while num>0: facto = facto*num num = num - 1 return facto # print(fact(5)) #// for checking # Defining power function def exp(num,po): ex = 1 while po>0: ex = ex*num po = po - 1 return ex # print(exp(2,8)) #// for checking # Implementation of Binomial Process # Probability of K arrivals with # probability of arrival as pr # not arrival probability is 1-pr # P = n!/(n-r)!*r! * p^r * (1-p)^n-r # r = k def Binomial(N,k,pr): BinCoef = (fact(N)/(fact(N-k)*fact(k))) ProRatio = (exp(pr,k)*exp(1-pr,N-k)) Probability = BinCoef*ProRatio return Probability N = 1 n = 1 k = 1 pr = 0.1 prn = 0.9 # Use of Vector to save data and # further algebric manipulation x = [] y = [] while n<40: x.append(n) y.append(Binomial(n,k,pr)) n = n + 1 pl.plot(x,y) print('Binomial Process Vector : ', y)

**Output:**

Binomial Process Vector : [0.1, 0.18000000000000002, 0.24300000000000005, 0.2916, 0.32805000000000006, 0.3542940000000001, 0.37200870000000014, 0.3826375200000001, 0.38742048900000015, 0.3874204890000002, 0.3835462841100002, 0.37657271530800024, 0.36715839742530026, 0.3558612159660602, 0.3431518868244152, 0.32942581135143856, 0.3150134321048131, 0.3001892705939984, 0.2851798070642985, 0.27017034353459857, 0.25531097464019564, 0.24072177608932738, 0.22649730750223074, 0.2127105148716602, 0.19941610769218143, 0.18665347679988184, 0.17444921100912034, 0.16281926360851232, 0.1517708135779347, 0.14130386091738747, 0.13141259065317037, 0.1220865358326228, 0.11331156606965304, 0.10507072490095098, 0.09734493630529284, 0.09011359817975681, 0.08335507831627505, 0.07704712644369205, 0.07116721416246292]

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