From 88763d7db3f803b9e5b6351e01c186a98e50bbf2 Mon Sep 17 00:00:00 2001
From: bnewbold
Date: Sun, 24 Jan 2010 08:07:57 +0000
Subject: tex math fixes

math/statistics.page  21 ++++++++++
1 file changed, 10 insertions(+), 11 deletions()
diff git a/math/statistics.page b/math/statistics.page
index 446450f..b3b5b3d 100644
 a/math/statistics.page
+++ b/math/statistics.page
@@ 4,7 +4,7 @@ Statistics
Basic Measures

The sample distribution has finite size and is what has been measured; the
parent distribution is inifinite and smooth and is the limit case of the
+parent distribution is infinite and smooth and is the limit case of the
sample distribution.
The mean, or average, is (of course):
@@ 25,7 +25,7 @@ probability of getting 'yes' for a single attempt.
$$P(x;n,p) = \frac{n!}{x! (nx)!} p^x (1p)^{nx}$$
The mean of this distribution is $\mu = np$, and $\sigma$ = \sqrt{np (1p)}.
+The mean of this distribution is $\mu = np$, and $\sigma = \sqrt{np (1p)}$.
Poisson Distribution

@@ 40,7 +40,7 @@ The classic! Also called a normal distribution.
$$P(x;\mu,\sigma) = \frac{1}{2\pi \sigma} e^{\left(\frac{(x\mu)^2}{2\sigma^2}\right)}$$
The mean is $\mu$ and the deviation is $\sigma=\sqrt(\mu)$.
+The mean is $\mu$ and the deviation is $\sigma=\sqrt{\mu}$.
Lorentzian Distribution

@@ 60,21 +60,20 @@ the error on the mean should get smaller. More elaborately, if the errors are
different for each individual measurement, the mean will be:
$$\bar{x}=
 \frac{ \sum_{i=1}^{N} x_i / \simga_{i}^2}{\sum_{i=1}^{N} 1/\simga_{i}^2}
 \pm \sqrt{ \frac{1}{\sum_{i=1}^{N} 1/\simga_{i}^2}}$$
+ \frac{ \sum_{i=1}^{N} x_i / \sigma_{i}^2}{\sum_{i=1}^{N} 1/\sigma_{i}^2}
+ \pm \sqrt{ \frac{1}{\sum_{i=1}^{N} 1/\sigma_{i}^2}}$$
$\Chi^2$ Distribution
+$\chi^2$ Distribution

$\Chi^2$ is often writen "chisquared" and is a metric for how well a fit
+$\chi^2$ is often written "chisquared" and is a metric for how well a fit
curve matches uncertain data.
$$\Chi^2 = \sum_{i=1}^{N}\left(\frac{x_i\mu_i}{\sigma{i}}\right)^2$$
+$$\chi^2 = \sum_{i=1}^{N}\left(\frac{x_i\mu_i}{\sigma{i}}\right)^2$$
The number of degrees of freedom of the system is the number of measurements
$N$ minus the number of variable parameters in a curve fit $N_c$: $\nu = NN_c$.
The reduced $\Chi^2$ value is $\Chi^{2}_r = \Chi^2 /\nu$. You want $\Chi^{2}_r$
+The reduced $\chi^2$ value is $\chi^{2}_r = \chi^2 /\nu$. You want $\chi^{2}_r$
to be around (but not exactly!) 1; if it is significantly larger there are
probably too many degrees of freedom, while if significantly smaller the fit is
bad.

+bad.
\ No newline at end of file

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