### Artificial IntelligenceAIMA Exercises

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 $t=2$.

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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