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(The proof involves calculating the CDF of A and w, then the joint CDF of A and w to get the CDF of X or Y, then differentiat to get the PDF of X or Y) | (The proof involves calculating the CDF of A and w, then the joint CDF of A and w to get the CDF of X or Y, then differentiat to get the PDF of X or Y) | ||
| − | + | Therefore, in c to produce a random variable with a gaussian distribution you simply do the following | |
<math>\sqrt(A) cos(drand48())</math> | <math>\sqrt(A) cos(drand48())</math> | ||
where A is what you solved for from part b of problem 1 | where A is what you solved for from part b of problem 1 | ||
Latest revision as of 18:03, 20 October 2008
We create variables :
A ~ exp(1/2)
w ~ unif[0, 2pi]
then let :
$ X = \sqrt(A)cos(w) $
$ Y = \sqrt(A)sin(w) $
Then you can go through the proof and show that the PDF of X and Y ~ N[0, 1] (The proof involves calculating the CDF of A and w, then the joint CDF of A and w to get the CDF of X or Y, then differentiat to get the PDF of X or Y)
Therefore, in c to produce a random variable with a gaussian distribution you simply do the following
$ \sqrt(A) cos(drand48()) $
where A is what you solved for from part b of problem 1
