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

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang