Advanced Brachytherapy Physics - Vienna 2016

The MC method … How do I sample RANDOMLY from a known probability distribution? There are numerous mathematical methods In example: . Inversion theorem Let x be a continuous random variable distributed over the interval [a, b] with a probability density function f(x) and a cumulative probability distribution function F(x) that is invertible. Given a random number, r, in the interval [0, 1], a value x * of x can be randomly selected according to:

Let x be a discrete random variable taking N values, x i

of probability, P i

so that:

Given a random number, r, in the interval [0, 1], a value x * of x can be randomly selected according to: x * = x j where j= min{ j: }