30 Dec

changes!

Hi! It’s been a while. How’s it going?

Around here, things are moving. They’re moving quickly. I’ve heard my professors say that a PhD is a weird time in life, because nothing really happens or changes for years in the middle of it, and then at the end EVERYTHING HAPPENS Read More

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