### Probability problem

There's a famous problem in probability: find a probability distribution such that two such independent random variables have a sum that is uniformly distributed from 0 to 1.

That turns out to be impossible. One way to prove it is by considering the expected value of exp(2*pi*i*x). Because the distribution of the sum has to have this quantity be 0, each part also has to have the same property. The only distribution with support between 0 and .5 with this property is 0 w.p .5, and 0.5 w.p. 0.5. That distribution doesn't work.

A related problem is: find a probability distribution such that two such independent random variables x1, and x2 satisfy x1 + 2*x2 is uniformly distributed from 0 to 1.

Can you do it?

## 3 Comments:

errr no but i loff u

Jer (er, Calvin),

I am probably the last person to know about probabilities, but I am guessing you are probably not doing much blogging these days.

Ran across the link so thought I would post a message to see if you are going to wait until Dec to update the site. You have so many great ideas, would encourage you to express them.

BTW glad #3 from 2007 has worked out for you!

Unk

testing, 1-2-3-2^2

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