Question

Say I want to generate random variables from the probability distribution

p={ 2-2x 0<x<1

0 . elsewhere

My scheme is to generate U's from [0,1],double them and plug them into the probability distribution. So U = 0.3 gives me p(0.6)=0.8 as random variable. Prove my idea is right or wrong.

Answer 1

Probability Density Function s given by:

,

           for 0 < x < 1

Cumulative Distribution Function F(x) is got by integrating f(x) from 0 to x as follows:

For generating random numbers following Probability Density Function f(x):

Generate random number u following Uniform Distribution in (0,1) and equate to F(x) as follows:

Solving this for x, we get:

,

where u is a random number in (0,1)

For example, for u = 0.3 gives you: