Over a million developers have joined DZone.
{{announcement.body}}
{{announcement.title}}

Monte Carlo Experiment

DZone's Guide to

Monte Carlo Experiment

Can you compute pi with random numbers? Read this article, it's worth the gamble!

· Performance Zone
Free Resource

Transform incident management with machine learning and analytics to help you maintain optimal performance and availability while keeping pace with the growing demands of digital business with this eBook, brought to you in partnership with BMC.

Monte Carlo simulations are a powerful way to solve a bunch of problems using random sampling. These include, and are not limited to, estimating computations that are costly in nature.

Here’s a fun way of computing value of π. Consider a circle of radius r centered at (0,0). This could be bound by a square with corners at (-r, -r), and (r, r). The area of the circle is πr² while the area of the binding square is 4r². If you were to randomly mark n points within the square, the probability p that it would be within the circle will be area of circle / area of square => π/4.

In a Monte Carlo experiment, you would randomly mark n points, and measure the probability p by counting the number of points within the circle. You have,

p/n = πr²/4r²

or

π = 4p/n.

Image title

Go to this page for a live demo of the experiment.

Try it out, you could see that the estimated value of π becomes better with n. Have fun!

Evolve your approach to Application Performance Monitoring by adopting five best practices that are outlined and explored in this e-book, brought to you in partnership with BMC.

Topics:
monte carlo ,pi ,experiment

Published at DZone with permission of Alosh Bennett, DZone MVB. See the original article here.

Opinions expressed by DZone contributors are their own.

{{ parent.title || parent.header.title}}

{{ parent.tldr }}

{{ parent.urlSource.name }}