Question

Consider the following experiment: generate a uniform random point (??, ??, ??) in a cube whose sides are of length 2, and then compute the distance from that random point to the center of the cube. If that distance is less than 1, you consider the experiment a success (assign an output of 1); otherwise it is a failure. Determine the long-run fraction of successes with this experiment, with a threshold for the standard deviation of the sample mean of 10−4. Using MATLAB

Answer 1

`Hey,

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clc%clears screen
clear all%clears history
close all%closes all files
format long
ct=0;
for i=1:10000
x=rand*2-1;
y=rand*2-1;
z=rand*2-1;
d=sqrt(x^2+y^2+z^2);
if(d<1)
out=true;
ct=ct+1;
else
out=false;
end
end
disp('Probability of winning is');
ct/10000

Kindly revert for any queries

Thanks.