From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 19 Aug 2019 01:58:27 +0000 (+1000)
Subject: [methods] continuous dist. & pdfs
X-Git-Tag: yr12~61
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/6ec015747c8d3c6e16759515afedb5c702896fa3?ds=inline

[methods] continuous dist. & pdfs
---

diff --git a/methods/statistics.tex b/methods/statistics.tex
index 56cd566..8ac24bf 100644
--- a/methods/statistics.tex
+++ b/methods/statistics.tex
@@ -174,4 +174,23 @@
 
   \[ \Pr(X \ge a) = 1 - \Pr(X < a) \]
 
+  \section{Continuous probability}
+
+  \subsection*{Continuous random variables}
+
+  \begin{itemize}
+    \item a variable that can take any real value in an interval
+  \end{itemize}
+
+  \subsection*{Probability density functions}
+
+  \begin{itemize}
+    \item area under curve \( = 1 \implies \int f(x) \> dx = 1\)
+    \item \(f(x) \ge 0 \forall x\)
+    \item pdfs may be linear
+    \item must show sections where \(f(x) = 0\) (use open/closed circles)
+  \end{itemize}
+
+  \[ Pr(a \le X \le b) = \int^b_a f(x) \> dx \]
+
 \end{document}