| (9 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | We create | + | We create variables : |
| − | + | A ~ exp(1/2) | |
| − | + | ||
| + | w ~ unif[0, 2pi] | ||
then let : | then let : | ||
| Line 9: | Line 10: | ||
<math>Y = \sqrt(A)sin(w)</math> | <math>Y = \sqrt(A)sin(w)</math> | ||
| + | |||
| + | 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 | ||
| + | |||
| + | <math>\sqrt(A) cos(drand48())</math> | ||
| + | |||
| + | where A is what you solved for from part b of problem 1 | ||
Latest revision as of 17:03, 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
