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Binomial Random Variables in C++
Random variables are those variables that are an outcome of the outcomes of a process that has the probability of giving rise to multiple outcomes. For example, The variable denoting head or tail as an outcome on tossing a coin is a random variable.
A binomial random variable is a special type of random variable whose value is related to an event that has a fixed probability of an outcome in an event.
There are certain properties that are possessed by a binomial random variable that makes it special. These are a must for a variable to become a binomial random variable −
The total number of outcomes is fixed.
The outcome of the trail is either true or false, nothing in between.
The probability of occurrence is the same on each trail.
No two trails are dependent on each other.
Binomial random variable probability
The probability of success of an outcome is given by the formula −
P (x= k ) = n! / k! (n-k)! * pk * (1-p)n-k
Based on this probability of a binomial random variable, the number of occurrences of the variable in the sample space.
E[X] = np
The variance of success is given by Var[X] = np (1-p)
Example
#include <iostream>
#include <cmath>
using namespace std;
int combination(int n, int r){
if (r > n / 2)
r = n - r;
int answer = 1;
for (int i = 1; i <= r; i++) {
answer *= (n - r + i);
answer /= i;
}
return answer;
}
float randombinomialProbability(int n, int k, float p){
return combination(n, k)*pow(p, k)*pow(1 - p, n - k);
}
int main(){
int n = 10;
int k = 5;
float p = 1.0 / 3;
float binomialRandomVariable = randombinomialProbability(n, k, p);
cout<<"Probability of "<<k;
cout<<" heads when a coin is tossed "<< n;
cout<<" times where probability of each head is "<<p;
cout<<" is = "<<binomialRandomVariable<<endl;
}Output
Probability of 5 heads when a coin is tossed 10 times where probability of each head is 0.333333 is = 0.136565
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