Consider the unit disk D= {(x, y)|a² + y² ≤1}, and the unit square S = [0,0] x [1,1]. Write a program that picks a random coordinate in S, and determines if this point is in D or not. If you repeat this experiment n times, let X be the number of times that the point was in S. Plot a figure showing the ratio X/n on the y-axis, and the number of trials, n, on the z-axis. Use many different values of n, up to at least n = 10,000. What do you expect this ratio to approach as n gets large?
Consider the unit disk D= {(x, y)|a² + y² ≤1}, and the unit square S = [0,0] x [1,1]. Write a program that picks a random coordinate in S, and determines if this point is in D or not. If you repeat this experiment n times, let X be the number of times that the point was in S. Plot a figure showing the ratio X/n on the y-axis, and the number of trials, n, on the z-axis. Use many different values of n, up to at least n = 10,000. What do you expect this ratio to approach as n gets large?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![5. Consider the unit disk D= {(x, y)² + y² ≤ 1}, and the unit square S = [0,0] × [1,1]. Write a program
that picks a random coordinate in S, and determines if this point is in D or not. If you repeat this
experiment n times, let X be the number of times that the point was in S. Plot a figure showing the
ratio X/n on the y-axis, and the number of trials, n, on the a-axis. Use many different values of n, up
to at least n = 10,000. What do you expect this ratio to approach as n gets large?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7289bb2-34de-4b7e-a86c-31e14a651d58%2F3c4a4750-70eb-42b2-9233-84f39814d01a%2Fs3aba3l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Consider the unit disk D= {(x, y)² + y² ≤ 1}, and the unit square S = [0,0] × [1,1]. Write a program
that picks a random coordinate in S, and determines if this point is in D or not. If you repeat this
experiment n times, let X be the number of times that the point was in S. Plot a figure showing the
ratio X/n on the y-axis, and the number of trials, n, on the a-axis. Use many different values of n, up
to at least n = 10,000. What do you expect this ratio to approach as n gets large?
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