20 Nov

This is a guest post by Prasad Patil that answers the question: how to put a shape in the margin of an R plot?

The help page for R’s par() function is a somewhat impenetrable list
of abbreviations that allow you to manipulate anything and everything

20 Nov

This is a guest post by Prasad Patil that answers the question: how to put a shape in the margin of an R plot?

The help page for R’s par() function is a somewhat impenetrable list
of abbreviations that allow you to manipulate anything and everything

04 Nov

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

04 Nov

This was originally written on Nov 25, 2013.

Converted from .tex using latex2wp.

In this note, we explained why the conditional expectation of a random variable ${Y}$ given a ${\sigma}$-field ${\mathscr{G}}$ can be seen as “smoothed version of ${Y}$ over ${\mathscr{G}}$” (in Example 2), and we briefly related the definition of conditional expectation Read More