Thatcher: A Nation Mourns

Posted in Politics on April 8, 2013 by telescoper

A Small Problemette related to Cosmological non-Gaussianity

Posted in Cute Problems, The Universe and Stuff with tags , , , on April 8, 2013 by telescoper

Writing yesterday’s post I remembered doing a calculation a while ago which I filed away and never used again. Now that it has come back to my mind I thought I’d try it out on my readers (Sid and Doris Bonkers). I think the answer might be quite well known, as it is in a closed form, but it might be worth a shot if you’re bored.

The variable $x$ has a normal distribution with zero mean and variance $\sigma^{2}$. Consider the variable

$y = x + \alpha \left( x^2 - \sigma^2 \right),$

where $\alpha$ is a constant. What is the probability density of $y$?