Hi there MHF
I've got this problem which I'm stuck on. I'm generating random uniformly distributed numbers between 0 and 1, and I need to transform these numbers into numbers governed by the probability density function
Apologies for not knowing LaTex, here's a picture .
f(y) = 0.2 for 0 < y ≤ 2
0.8y - 1.4 for 2 < y ≤ 3
I believe the first thing I need to do is figure out the cumulative distribution function F(y), for this I came up with
Next I think I need to find the transformation functions for 0 < y ≤ 2 and 2 < y ≤ 3. So by substituting the uniform variable U in I can get for the first segment, however for the second segment (2 < y ≤ 3) I get two quadratics here (wolfram link) so I'm not sure if this is the right track or not.
f(y) = 0.2y for 0 < y ≤ 2
0.4y^2 - 1.4y + 1.6 for 2 < y ≤ 3
1 3 < y
Basically my understanding of how transforming these variables works goes like this
1) Generate uniform random variable U
2) If U is less than 0.4 (which I got from subbing y=2 into 0.2y), it is transformed using . Otherwise if U is greater than 0.4 it is transformed using one of the quadratics in the above link.
Anyone able to help me out here? Much appreciated