From 36fb90f69e28c8fec1e67bdc468a792f69114539 Mon Sep 17 00:00:00 2001
From: Mart Lubbers <mart@martlubbers.net>
Date: Tue, 6 Jan 2015 10:02:47 +0100
Subject: [PATCH] explanations added

---
 report/ass2-1.tex | 40 +++++++++++++++++++++++++++++++---------
 report/d1.dot     |  5 ++---
 2 files changed, 33 insertions(+), 12 deletions(-)

diff --git a/report/ass2-1.tex b/report/ass2-1.tex
index 964ec1e..4ae080f 100644
--- a/report/ass2-1.tex
+++ b/report/ass2-1.tex
@@ -6,17 +6,33 @@
 	\includegraphics[scale=0.5]{d1.eps}
 \end{figure}
 
-\strut\\
+We introduced a \textit{Noisy OR} to represent the causal independence of
+\textit{Burglar} and \textit{Earthquake} on Alarm. Probabilities for the causes
+of the alarm are calculated using days, in practice this means that the
+smallest discrete time interval is one day. The calculation for the probability
+of a burglar is then calculated with the following formula(taking leap years
+into account and assuming a standard gregorian calendar).
+$$\frac{1}{365 + 0.25 - 0.01 - 0.0025}=\frac{1}{365.2425}$$
+
+This gives the following probability distributions\\
 \begin{tabular}{|l|ll|}
 	\hline
-	& \multicolumn{2}{c|}{Radio}\\
-	Earthquake & T & F\\
+	& \multicolumn{2}{c|}{Earthquake}\\
 	\hline
-	T & $0.9998$ & $0.0002$\\
-	F & $0.0002$ & $0.9998$\\
+	T & $0.0027$ & $0.9972$ \\
+	F & $0.9973$ & $0.0027$\\
 	\hline
 \end{tabular}
 %
+\begin{tabular}{|l|ll|}
+	\hline
+	& \multicolumn{2}{c|}{Burglar}\\
+	\hline
+	T & $0.0027$ & $0.9973$ \\
+	F & $0.9973$ & $0.0027$\\
+	\hline
+\end{tabular}
+
 \begin{tabular}{|l|ll|}
 	\hline
 	& \multicolumn{2}{c|}{$I_1$}\\
@@ -26,7 +42,6 @@
 	F & $0$ & $1$\\
 	\hline
 \end{tabular}
-%
 \begin{tabular}{|l|ll|}
 	\hline
 	& \multicolumn{2}{c|}{$I_2$}\\
@@ -36,7 +51,6 @@
 	F & $0$ & $1$\\
 	\hline
 \end{tabular}
-%
 \begin{tabular}{|ll|ll|}
 	\hline
 	&& \multicolumn{2}{c|}{Burglar}\\
@@ -48,7 +62,7 @@
 	F & F & $0$ & $1$\\
 	\hline
 \end{tabular}
-%
+
 \begin{tabular}{|l|ll|}
 	\hline
 	& \multicolumn{2}{c|}{Watson}\\
@@ -58,7 +72,6 @@
 	F & $0.4$ & $0.6$\\
 	\hline
 \end{tabular}
-%
 \begin{tabular}{|l|ll|}
 	\hline
 	& \multicolumn{2}{c|}{Gibbons}\\
@@ -68,3 +81,12 @@
 	F & $0.04$ & $0.96$\\
 	\hline
 \end{tabular}
+\begin{tabular}{|l|ll|}
+	\hline
+	& \multicolumn{2}{c|}{Radio}\\
+	Earthquake & T & F\\
+	\hline
+	T & $0.9998$ & $0.0002$\\
+	F & $0.0002$ & $0.9998$\\
+	\hline
+\end{tabular}
diff --git a/report/d1.dot b/report/d1.dot
index 29cf034..5d45301 100644
--- a/report/d1.dot
+++ b/report/d1.dot
@@ -3,16 +3,15 @@ digraph {
 	i2 [label=<I<SUB>2</SUB>>]
 	n [shape=plaintext label="Noisy OR"]
 	n -> alarm [style=invis]
-	newscast [label="Newcast calls"]
 	gibbons [label="Gibbons calls"]
 	watson [label="Watson calls"]
+	newscast [rank=max label="Newcast calls"]
 	
 	earthquake -> i1
 	burglar -> i2
 	i1 -> alarm
 	i2 -> alarm
-	earthquake -> newscast
-
 	alarm -> watson
 	alarm -> gibbons
+	earthquake -> newscast
 }
-- 
2.20.1