Question

Give an algorithm to generate random variates from the following probability density function.

f(x) = 2x/3 if 0<=x<=1

=1-x/3 if 1<=x<=3

Answer 1

To generate an algorithm to generate a random variate, we compute the cumulative distributive function here as:

F(1) = 1/3

For x > 1,

Therefore the CDF for X here is obtained as:

Now to create a random variable,

First step is to select a number from the uniform distribution (0,1)

Let it be 0.2 for example.

Now for 0.2, we obtain the random number from the distribution as:

Therefore 0.7746 is one of the random number here.

This is how we can obtain any random variate from the given uniform distribution (0,1)