Physics307L:Schedule/Week 12 agenda/PDFs

Contents

General case

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,

$\ t_i = -\tau \ln r_i$