S09.1 Buffon's Needle & Monte Carlo Simulation
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- Опубліковано 15 вер 2024
- MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: ocw.mit.edu/RE...
Instructor: John Tsitsiklis
License: Creative Commons BY-NC-SA
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This is the best and most in depth video I found about the problem. Also the only one that doesn't make unnecessary simplifications. Thank you.
All the videos of this course are awesome. All the concepts are so easy to understand in this course.
John Tsitsiklis is amazing !!
THANK YOU JOHN !! THANK YOU MIT !!
An absolutely beautiful and profound result explained by an exceptionally talented teacher!!
great teacher does not say too many words，but everyword they say count
it blew my mind when I got to know we found the value of pi using complete randomness. Amazing problem and an amazing explanation.
Thank you so much! And the accent makes it even better!
I'm loving these classes. This one is particularly good. Thanks professor Tsitsiklis and MIT.
Big thanks for this video. That help me from France 🇫🇷 thanks 🙏🏻
Very nice example. Clarified a lot of fundamentals. Thanks for it.
I agree the range of the variable x is 0
Well, basically the range depends on what theta represents. In the video, theta is the smallest angle formed by the line and the needle. in your suggestion, it is the angle, not the smallest one, so 0
Awesome! Thanks for your clever explanation.
Some kind of magic
thank you for savig us, my lord
16:10 : Supplementary* instead of complementary
So neat explanation
Thank you professor .
Thank you
This problem may be simplified by assuming a coin radius r instead of a needle. In this case we won't be needed in PDF at all and such problem will be solved geometrically. An interesting special case, isn't it? Moreover, there is a geometrical solution for the original problem.
jesus !! wow
Awesome
Why does x vary from 0 to d/2? Shouldn't it vary from 0 to d?
x is the distance from the nearest line. It is greatest when the needle mid-point is exactly at the mid-point of 2 lines.
How do you work out the uniform distribution of x and theta? What do you integrate?
X has a range of [0, d/2]. So the uniform PDF should be 1/(d/2 - 0) = 2/d. Similarly, theta should be 1/(pi/2 - 0) = 2/pi.
In 10:23, Can someone explain why P(X
essentially, the double integral represent the whole sample space (all the possibilities of the needles) if we do not set up lower & upper bounce , which means all the joint possibilities of f_{X,\theta} (x, \theta). However, we want to find P(X
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