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):

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

Numerically solving for x gives random number with appropriate distribution.

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
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