Initial import

README.md

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+# math
+
+These are some miscellaneous math functions implemented in Javascript that helped me with various assignments.
+
+## Distributions
+The `distributions.js` file has some functions relating to Binomial and Poisson distributions of random variables.
+

distributions.js

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+/**
+ * Some functions for calculating distributions of random variables.
+ */
+
+/**
+ * Takes the factorial of n.
+ * @param {number} n
+ * @return {number}
+ */
+const fact = n => {
+    if ( n == 0 || n == 1 ) return 1
+
+    for ( let i = n - 1; i >= 1; i -= 1 ) {
+        n = n * i
+    }
+
+    return n
+}
+
+/**
+ * Compute the {n}\choose{k} value.
+ * @param {number} n the total number of items
+ * @param {number} k the number to take at a time
+ * @return {number}
+ */
+const choose = (n,k) => (fact(n))/(fact(k)*(fact(n-k)))
+
+/**
+ * Calculate the binomial distribution of a random variable:
+ *
+ * b(x; n,p) for lower_x <= x <= upper_x
+ */
+const binom_range = (lower_x, upper_x, n, p) => {
+    let sum = 0
+
+    for ( let i = lower_x; i <= upper_x; i += 1 ) {
+        sum += choose(n, i) * Math.pow(p, i) * Math.pow(1-p, n-i)
+    }
+
+    return sum
+}
+
+/**
+ * Calculate the binomial distribution for some specific x.
+ *
+ * b(x; n,p)
+ */
+const binom_dist = (x, n, p) => choose(n, x) * Math.pow(p, x) * Math.pow(1-p, n-x)
+
+/**
+ * Calculate the poisson distribution for some specific x.
+ *
+ * p(x, lambda * t)
+ */
+const poisson_dist = (x, lambda, t) => {
+    const numerator = Math.pow(Math.E, -1 * lambda * t) * Math.pow(lambda * t, x)
+    const denom = fact(x)
+    return numerator / denom
+}
+
+/**
+ * Calculate the poisson range for some specific x:
+ *
+ * p(x, lambda * t) for lower_x <= x <= upper_x.
+ */
+const poisson_range = (lower_x, upper_x, lambda, t) => {
+    let sum = 0
+
+    for ( let i = lower_x; i <= upper_x; i += 1 ) {
+        sum += poisson_dist(i, lambda, t)
+    }
+
+    return sum
+}
+
+module.exports = exports = {fact, choose, binom_range, binom_dist, poisson_dist, poisson_range}