mshron

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <title>Square transformations</title>

mshron

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <title>Square transformations</title>

mshron

<title>Square transformations</title>

mshron

Suppose I have a random variable $Y$ with $F_Y(y) = \sqrt{y}$ on $y\in[0,1]$. It's a CDF because it is 0 as $y \rightarrow -\infty$, 1 as $y \rightarrow \infty$, increasing, and continuous.

The PDF should be $f_Y (y)= \frac{1}{2\sqrt{y}}$, since all we're doing is differentiating the CDF.

But $f_Y(0) = \infty$ while $F_y(0) = 0$. The PDF doesn't seem well defined. And even if we start at some $\epsilon &gt; 0$ instead of at 0, we're still in a weird spot where the PDF starts out very very high but the CDF grows at a reasonable-looking rate.

They don't seem to have the right relationship. What's going on here? Did I mess something up with the continuity somehow?

mshron

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I hereby claim:

• I am mshron on github.
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To claim this, I am signing this object:

mshron

### MATPLOTLIBRC FORMAT

### This is a custom config based on huyng's gist: https://gist.github.com/816622


#### CONFIGURATION BEGINS HERE

# the default backend; one of GTK GTKAgg GTKCairo CocoaAgg FltkAgg
# MacOSX QtAgg Qt4Agg TkAgg WX WXAgg Agg Cairo GDK PS PDF SVG Template
# You can also deploy your own backend outside of matplotlib by