A quantity has probability density on the interval and zero elsewhere
PHYSICS · Subjective · Fermi University Physics · Computational Physics · Monte Carlo and lattice simulation of physical systems · Monte Carlo and lattice simulation of physical systems
Computational Physics, Ch Drawing numbers: random walks and Monte Carlo
Problem
A quantity x has probability density P(x)=2x on the interval [0,1] and zero elsewhere.
(a) Derive the cumulative distribution function F(x).
(b) Derive the inverse-transform sampling rule x=F−1(u) for drawing x from a uniform draw u∈[0,1).
(c) Use the rule to find the value of x produced by the draw u=0.81.