Write code in python to find pi value (Monte Carlo Method) Plot how well the approximation is according to size of your sample (number of point)
Added by Samuel R.
Close
Step 1
Import the necessary libraries: ```python import random import matplotlib.pyplot as plt ``` Show more…
Show all steps
Your feedback will help us improve your experience
Liliane Martins and 61 other AP CS educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The Write a C++ program to estimate PI using the Monte Carlo method. Your program should ask the user to input the total number of random points (xi, yi) we will generate in the simulation. Use ‐srand(time(0))‐ function. Define PI = 3.14159265. Estimate PI value(10 digits of precision) and the error(5 digits of precision) when you use 10^3 ,10^4, 10^5 and 10^6 samples. error = [(estimated_PI – true_PI) / true_PI] * 100% After you find the value of Pi, use that to find the area of an ellipse with semi-major axis as 10 and semi minor-axis of 7, and report the ‐estimated PI value‐, ‐error‐, ‐estimated ellipse area‐ simultaneously. For example, Hint: Ellipse area = π*a*b Please enter the total number of random points 'n' in the simulation: 1000 The estimated pi value is 3.1119999886 with n = 1000. The error is -0.94197% The estimated ellipse area is: 217.84000 Please enter the total number of random points 'n' in the simulation: 1000000 The estimated pi value is 3.1402640343 with n = 1000000. The error is -0.04229% The estimated ellipse area is: 219.81848 Your work starts here. Code: Results: Your answer ends here.
Supreeta N.
Use Euler's method to calculate the first three approximations to the given initial value problem for the specified increment size. Calculate the exact solution and investigate the accuracy of your approximations. Round your results to four decimal places. $y^{\prime}=x(1-y), \quad y(1)=0, \quad d x=0.2$
First-Order Differential Equations
Solutions Slope Fields and Eulers Method
Use Euler's method to calculate the first three approximations to the given initial value problem for the specified increment size. Calculate the exact solution and investigate the accuracy of your approximations. Round your results to four decimal places. $y^{\prime}=\frac{2 y}{x}, \quad y(1)=-1, \quad d x=0.5$
Recommended Textbooks
Computer Science and Information Technology
Introduction to Programming Using Python
Computer Science - An Overview
Watch the video solution with this free unlock.
EMAIL
PASSWORD