Explore >> Select a destination
|
You are here 
|
almostsuremath.com | ||
| | | | |
jmanton.wordpress.com
|
|
| | | | | If $latex Y$ is a $latex \sigma(X)$-measurable random variable then there exists a Borel-measurable function $latex f \colon \mathbb{R} \rightarrow \mathbb{R}$ such that $latex Y = f(X)$. The standard proof of this fact leaves several questions unanswered. This note explains what goes wrong when attempting a "direct" proof. It also explains how the standard proof... | |
| | | | |
xorshammer.com
|
|
| | | | | In the book A=B, the authors point out that while the identity $latex \displaystyle{\sin^2(|10 + \pi x|) + \cos^2(|10 + \pi x|) = 1}$ is provable (by a very simple proof!), it's not possible to prove the truth or falsity of all such identities. This is because Daniel Richardson proved the following: Let $latex \mathcal{R}$... | |
| | | | |
mkatkov.wordpress.com
|
|
| | | | | For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... | |
| | | | |
dismalsci.wordpress.com
|
|
| | | As an experiment, I have recently started using Vim as my primary text editor. While I have been an Emacs aficionado for a very, very long time - clocking in at almost 16 years - Vim is something that I have always been curious about, and tinkered with from time to time, while ending up... | ||
