04 Nov

Why probability density function can be seen as density of a measure with respect to another measure – an example of N(0,1)

This was originally written on Nov 3, 2013.

Converted from .tex using latex2wp.

Usually, we say a random variable {X} follows a Normal(0,1) distribution, if its cumulative distribution can be expressed as:

\displaystyle P\{X\leq t\}=\int_{-\infty}^{t}\frac{1}{\sqrt{2\pi}}e^{-\frac{x^{2}}{2}}dx.

Now we formalize this in a more measure-theoretic way, in correspondence to what we learned in the course, particularly, Read More