Physics307L F07:Schedule/Week 12 agenda/PDFs
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Lots of algorithms available for generating random numbers from 0 to 1 with uniform probability
General case
Assume you have a random number r from 0 to 1. To transform to x, with PDF given by P(x):
- [math]\displaystyle{ r=\int_{X=-\infty}^{x} P(x)\, dx }[/math]
Numerically solving for x gives random number with appropriate distribution.
Specific case, time for random event to occur (i.e. radioactive decay)
- [math]\displaystyle{ P(t) = \frac {1}{\tau} e^{-\frac{t}{\tau}} }[/math]
Solving above,
- <math>\ t_i = -\tau \ln r_i
