uniform degeneration

Last modified by Nikita Kapchenko on 2019/12/19 13:30

For any random variable Unknown macro: formula. Click on this message for details.
 with its CDF Unknown macro: formula. Click on this message for details.
 

We always have Unknown macro: formula. Click on this message for details.

Proof.

Define random variable Unknown macro: formula. Click on this message for details.
with unknown yet distribution function Unknown macro: formula. Click on this message for details.

Unknown macro: formula. Click on this message for details.
some constant

Unknown macro: formula. Click on this message for details.

So by definition of uniform distribution Unknown macro: formula. Click on this message for details.

Check wikipedia for more info