Class Meeting 04: Estimating the State of a Door (Bayes Filter Algorithm) Exercise Solutions

This page contains solutions for the door state estimation class exercise during for Class Meeting 04.

Belief calculation for $t=2$

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$\overline{bel}(X_2=\text{is\_open})=1\cdot 0.75+0.8\cdot 0.25=0.95$
$\overline{bel}(X_2=\text{is\_closed})=0\cdot 0.75+0.2\cdot 0.25=0.05$

$bel(X_2=\text{is\_open})=\eta 0.6\cdot 0.95\approx 0.983$
$bel(X_2=\text{is\_closed})=\eta 0.2\cdot 0.05\approx 0.017$