Physics307L:Schedule/Week 12 agenda/PDFs

Assume you have a random number r from 0 to 1. To transform to x, with PDF given by P(x):

 * $$r=\int_{X=-\infty}^{x} P(x)\, dx$$

Specific case, time for random event to occur (i.e. radioactive decay)

 * $$P(t) = \frac {1}{\tau} e^{-\frac{t}{\tau}}$$

Solving above,

 * \ t_i = -\tau \ln r_i