feat: added binomial_dist.cpp

probability/binomial_dist.cpp

@@ -0,0 +1,81 @@
+#include <iostream>
+#include <cmath>
+
+// the binomial distribution models the number of
+// successes in a sequence of n independent events
+
+// n : number of trials
+// p : probability of success
+// x : desired successes
+
+// finds the expected value of a binomial distribution
+
+double binomial_expected(double n, double p) {
+    return n * p;
+}
+
+// finds the variance of the binomial distribution
+
+double binomial_variance(double n, double p) {
+    return n * p * (1 - p);
+}
+
+// finds the standard deviation of the binomial distribution
+
+double binomial_standard_deviation(double n, double p) {
+    return sqrt(binomial_variance(n, p));
+}
+
+// Computes n choose r
+// n being the trials and r being the desired successes
+
+double nCr(double n, double r) {
+    double numerator = n;
+    double denominator = r;
+
+    for (int i = n - 1 ; i >= ((n - r) + 1); i--) {
+        numerator *= i;
+    }
+
+    for (int i = 1; i < r ; i++) {
+        denominator *= i;
+    }
+
+    return numerator / denominator;
+}
+
+// calculates the probability of exactly x successes
+
+double binomial_x_successes(double n, double p, double x) {
+    return nCr(n, x) * pow(p, x) * pow(1-p, n-x);
+}
+
+// calculates the probability of a result within a range (inclusive, inclusive)
+
+double binomial_range_successes(
+    double n, double p, double lower_bound, double upper_bound) {
+    double probability = 0;
+    for (int i = lower_bound; i <= upper_bound; i++) {
+        probability += nCr(n, i) * pow(p, i) * pow(1 - p, n - i);
+    }
+    return probability;
+}
+
+int main() {
+    std::cout << "expected value : "
+        <<binomial_expected(100, 0.5) << std::endl;
+
+    std::cout << "variance : "
+        << binomial_variance(100, 0.5) << std::endl;
+
+    std::cout << "standard deviation : "
+        << binomial_standard_deviation(100, 0.5) << std::endl;
+
+    std::cout << "exactly 30 successes : "
+        << binomial_x_successes(100, 0.5, 30) << std::endl;
+
+    std::cout << "45 or more successes : "
+        << binomial_range_successes(100, 0.5, 45, 100) << std::endl;
+
+    return 0;
+}