From 7781d5b746eda31947b81e66355ade3a59494bff Mon Sep 17 00:00:00 2001
From: Varun <1990.singlav@gmail.com>
Date: Sun, 23 Feb 2020 00:19:23 +0530
Subject: [PATCH 1/2] extend estimation of area under curve of y=x using monte
 carlo simulation to any given lower and upper bound

---
 maths/monte_carlo.py | 26 +++++++++++++++++---------
 1 file changed, 17 insertions(+), 9 deletions(-)

diff --git a/maths/monte_carlo.py b/maths/monte_carlo.py
index 4980c5c55c8c..6e1084c96d4a 100644
--- a/maths/monte_carlo.py
+++ b/maths/monte_carlo.py
@@ -42,29 +42,37 @@ def area_under_line_estimator(iterations: int,
     An implementation of the Monte Carlo method to find area under
        y = x where x lies between min_value to max_value
     1. Let x be a uniformly distributed random variable between min_value to max_value
-    2. Expected value of x = integration of x from min_value to max_value
+    2. Expected value of x = (integration of x from min_value to max_value) / (max_value - min_value)
     3. Finding expected value of x:
         a. Repeatedly draw x from uniform distribution
         b. Expected value = average of those values
-    4. Actual value = 1/2
+    4. Actual value = (max_value^2 - min_value^2) / 2
     5. Returns estimated value
     """
-    return mean(uniform(min_value, max_value) for _ in range(iterations))
+    return mean(uniform(min_value, max_value) for _ in range(iterations)) * (max_value - min_value)
 
 
-def area_under_line_estimator_check(iterations: int) -> None:
+def area_under_line_estimator_check(iterations: int,
+                                    min_value: float=0.0,
+                                    max_value: float=1.0) -> None:
     """
     Checks estimation error for area_under_line_estimator func
     1. Calls "area_under_line_estimator" function
     2. Compares with the expected value
     3. Prints estimated, expected and error value
+    
+    >>> area_under_line_estimator_check(100, 0, 2)
+    >>> area_under_line_estimator_check(100)
     """
-    estimate = area_under_line_estimator(iterations)
+    
+    estimated_value = area_under_line_estimator(iterations, min_value, max_value)
+    expected_value = (max_value*max_value - min_value*min_value) / 2
+    
     print("******************")
-    print("Estimating area under y=x where x varies from 0 to 1")
-    print("Expected value is ", 0.5)
-    print("Estimated value is ", estimate)
-    print("Total error is ", abs(estimate - 0.5))
+    print("Estimating area under y=x where x varies from ",min_value, " to ",max_value)
+    print("Estimated value is ", estimated_value)
+    print("Expected value is ", expected_value)
+    print("Total error is ", abs(estimated_value - expected_value))
     print("******************")
 
 

From 2bf88a373fcb48d029c1a3bf490e075bf1820804 Mon Sep 17 00:00:00 2001
From: Varun <1990.singlav@gmail.com>
Date: Sun, 23 Feb 2020 00:32:23 +0530
Subject: [PATCH 2/2] remove doctest

---
 maths/monte_carlo.py | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/maths/monte_carlo.py b/maths/monte_carlo.py
index 6e1084c96d4a..6a407e98badd 100644
--- a/maths/monte_carlo.py
+++ b/maths/monte_carlo.py
@@ -60,9 +60,6 @@ def area_under_line_estimator_check(iterations: int,
     1. Calls "area_under_line_estimator" function
     2. Compares with the expected value
     3. Prints estimated, expected and error value
-    
-    >>> area_under_line_estimator_check(100, 0, 2)
-    >>> area_under_line_estimator_check(100)
     """
     
     estimated_value = area_under_line_estimator(iterations, min_value, max_value)