Example 1

Simulate a non-uniform distribution P(x)=2x, xɬ

with uniform random generator.

Step 1. Solve

u = = x2

? x =

Step 2. Generate a uniform r.v. x (value in [0, 1]) using

generator in C, C++, Java, Minitab or SAS etc.

Step 3. Calculate x through equation from Step 1.

Step 4. Repeat Step 2 & 3 n times (e.g. 1000 observations).

[Step 5.] Calculate mean and standard deviation etc.