Question

I have this (pseudocode):

var a = Math.random(); // returns random number from 0 to 1

I would like to have greater probability of selecting lower numbers just like picture describes. How should equation (code) look like?

Answer 1

The easiest here is to proceed with Rejection sampling.

Basically you simulate a bi-dimensional variable (x,y) = (Math.random(), Math.random()). It is a point in the square [0,1][0,1]. If the variable (x,y) is in the triangle you drawn, then take x.

x will have the distribution you are looking for.

Pseudocode:

x = Math.random();
y = Math.random();

if x+y < 1:
   return x;

You could actually get away with it by drawing only one random variable (by computing and inverting the Cumulative Distribution Function), but that’s much more complicated in this case.