feat: binomial distribution

src/main.py

@@ -3,11 +3,17 @@ from sympy import diff, limit, oo, symbols
 from modules.math import (
 	test_math_module
 )
+from modules.probability import (
+	test_probability_module
+)
 from modules.strings import t_strings
 
 if __name__=="__main__":
 	t_strings()
 
 	print(">> Math module")
-	test_math_module()
+	# test_math_module()
+	print(">>>>>>>>>>>>>>>>>>>>")
+	print(">> Probability module")
+	test_probability_module()
 	print(">>>>>>>>>>>>>>>>>>>>")

src/modules/probability.py

@@ -2,9 +2,41 @@
 ##  "Essential Math for Data Science" - Thomas Nield
 ##  Chaper 2 - Probability 
 
+from scipy.stats import binom
+from math import factorial
+
 # 2.0 odds means than an events has twice the probabilities to happen than not
 def p_odds_to_probability(o):
 	return  (o / (1 + o))
 
 def p_probability_to_odds(p):
 	return (p / (1 - p))
+
+## Binomial distribution
+def p_binomial_distribution_example():
+	n = 10
+	p = 0.9
+
+	for k in range(n + 1):
+		probability = binom.pmf(k, n, p)
+		print("{0} >> {1}".format(k, probability))
+
+def binomial_coeficient(pool, count):
+	return factorial(pool) / (factorial(count) * factorial(pool - count))
+
+def p_binomial_distribution_scratch(p, n):
+	# For each number calc the probability of that exact number of outcomes (no order)
+	for k in range(n + 1):
+		# 1. Simple combinatory with the binomial coeficient (combinations of k elements out of a pool of n without repetition without order)
+		combinatory = binomial_coeficient(n, k)	
+		# 2. Probability of success, the probability of making it k times
+		probability_of_success = p ** k # p * p, k times
+		# 3. Probability of failure, inverse of the success
+		probability_of_failure = (1 - p) ** (n - k) # inverse of probability the rest of the times
+		k_binomital_distribution_probability = combinatory * probability_of_success * probability_of_failure
+		print("[{0}]: {1}".format(k, k_binomital_distribution_probability))
+
+
+def test_probability_module():
+	p_binomial_distribution_example()
+	p_binomial_distribution_scratch(0.9, 10)