Exercise 15.17

For the DBN specified in Exercise sleep1-exercise and for the evidence values

$\textbf{e}_1 = not\space red\space eyes,\space not\space sleeping\space in\space class$ $\textbf{e}_2 = red\space eyes,\space not\space sleeping\space in\space class$ $\textbf{e}_3 = red\space eyes,\space sleeping\space in\space class$

perform the following computations:

1. State estimation: Compute $P({EnoughSleep}_t | \textbf{e}_{1:t})$ for each of $t = 1,2,3$.

2. Smoothing: Compute $P({EnoughSleep}_t | \textbf{e}_{1:3})$ for each of $t = 1,2,3$.

3. Compare the filtered and smoothed probabilities for $t=1$ and $t=2$.