X-Git-Url: https://git.martlubbers.net/?a=blobdiff_plain;f=report%2Fass2-1.tex;h=0ad812b9842c758b0ab492fbc40c76ced785c078;hb=1de4e50f5b42d6bace74061193939fe87f74c9f9;hp=964ec1e1632301d9edcf790ef2ac3c9802cc87e4;hpb=7a3d4d10b9911874ae4ef6b39b320f071f21c05e;p=ker2014-2.git diff --git a/report/ass2-1.tex b/report/ass2-1.tex index 964ec1e..0ad812b 100644 --- a/report/ass2-1.tex +++ b/report/ass2-1.tex @@ -6,27 +6,42 @@ \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|}{$I_1$}\\ Earthquake & T & F\\ \hline - T & $0.2$ & $0.08$\\ + T & $0.2$ & $0.8$\\ F & $0$ & $1$\\ \hline \end{tabular} -% \begin{tabular}{|l|ll|} \hline & \multicolumn{2}{c|}{$I_2$}\\ @@ -36,11 +51,10 @@ F & $0$ & $1$\\ \hline \end{tabular} -% \begin{tabular}{|ll|ll|} \hline - && \multicolumn{2}{c|}{Burglar}\\ - i1 & i2 & T & F\\ + && \multicolumn{2}{c|}{Alarm}\\ + $I_1$ & $I_2$ & T & F\\ \hline T & T & $1$ & $0$\\ T & F & $1$ & $0$\\ @@ -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}