This page contains solutions for the door state estimation class exercise during for Class Meeting 03.
\(\overline{bel}(X_2 = \textrm{is_open}) = 1 \cdot 0.75 + 0.8 \cdot 0.25 = 0.95 \)
\(\overline{bel}(X_2 = \textrm{is_closed}) = 0 \cdot 0.75 + 0.2 \cdot 0.25 = 0.05 \)
\(bel(X_2 = \textrm{is_open}) = \eta \: 0.6 \cdot 0.95 \approx 0.983 \)
\(bel(X_2 = \textrm{is_closed}) = \eta \: 0.2 \cdot 0.05 \approx 0.017 \)