tex math fixes

1 files 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.
 
 $$P(x;n,p) = \frac{n!}{x! (n-x)!} p^x (1-p)^{n-x}$$
 
-The mean of this distribution is $\mu = np$, and $\sigma$ = \sqrt{np (1-p)}.
+The mean of this distribution is $\mu = np$, and $\sigma = \sqrt{np (1-p)}$.
 
 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 "chi-squared" and is a metric for how well a fit 
+$\chi^2$ is often written "chi-squared" 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 $N_c$: $\nu = N-N_c$.
 
-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