Calculate P(A > B) and P(A = B), where A and B are independent Poisson variables.

test.cpp

#include <iostream>
#include <cmath>
using namespace std;

double pXy(double x, double y, int N);
double pxy(double x, double y, int N);

int main(void) {
    double pAb,paB,pab,a,b;
    int N;
    cout << "Assume that Poisson r.v. A and B are indepedent" << endl;
    cout << "Parameter for A: ";
    cin >> a;
    cout << "Parameter for B: ";
    cin >> b;
    cout << "Number of terms to be added (100 <= N <= 1000): ";
    cin >> N;
    pAb = pXy(a,b,N);
    paB = pXy(b,a,N);
    pab = pxy(a,b,N);
    cout << "P(A > B) = " << pAb << ", P(A < B) = " << paB <<
        ", P(A = B) = " << pab << endl;
}

/* P(X > Y) */
double pXy(double x, double y, int N) {
    double ans = 0;
    for (int i = 1; i <= N; i++) {
        for (int j = 0; j < i ; j++) {
            double term = 1;
            for (int k = 1; k <= i; k++)
                term *= x / k;
            for (int k = 1; k <= j; k++)
                term *= y / k;
            ans += term;
        }
    }
    return ans * exp(-x - y);
}

/* P(X = Y) */
double pxy(double x, double y, int N) {
    double ans = 0;
    for (int i = 0; i <= N; i++) {
        double term = 1;
        for (int k = 1; k <= i; k++)
            term *= x / k * y / k;
        ans += term;
    }
    return ans * exp(-x - y);
}