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 $t=2$.
$$ \textbf{e}_1 = not\space red\space eyes,\space not\space sleeping\space in\space class $$ $$ \textbf{e}_2 = red\space eyes,\space not\space sleeping\space in\space class $$ $$ \textbf{e}_3 = red\space eyes,\space sleeping\space in\space class $$ 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 $t=2$.