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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 $t=2$.