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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 $t=2$.

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