S09.1 Buffon's Needle & Monte Carlo Simulation
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- čas přidán 23. 04. 2018
- MIT RES.6-012 Introduction to Probability, Spring 2018
View the complete course: ocw.mit.edu/RES-6-012S18
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.
it blew my mind when I got to know we found the value of pi using complete randomness. Amazing problem and an amazing explanation.
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 !!
great teacher does not say too many words，but everyword they say count
An absolutely beautiful and profound result explained by an exceptionally talented teacher!!
I'm loving these classes. This one is particularly good. Thanks professor Tsitsiklis and MIT.
Thank you so much! And the accent makes it even better!
Very nice example. Clarified a lot of fundamentals. Thanks for it.
Awesome! Thanks for your clever explanation.
Big thanks for this video. That help me from France 🇫🇷 thanks 🙏🏻
thank you for savig us, my lord
Some kind of magic
So neat explanation
Thank you professor .
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
Thank you
Awesome
16:10 : Supplementary* instead of complementary
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.
jesus !! wow
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.
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.
👌
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