Consider the following training data for a sentiment analysis classifier for movie reviews.

Review Class

this a fun movie about a couple in love $.$ Positive

this movie is packed with action $.$ Positive

biggest disappointment of the year $.$ Negative

Part $1)$ Based on this data, compute the following marginal probabilities $($these are also called the prior probabilities$)$:

Pr$($y$=+)=?$

Pr$($y$=-)=?$

Part $2)$ Based on this data, what is Pr$($y$=+|$movie of the year $.)$ for a Naive Bayes classifier? Use add

$=1$ smoothing.

Recall that for a Naive Bayes classifier:

and

Part $3)$ Based on this data, what is Pr$($y$=-|$movie of the year $.)$ for a Naive Bayes classifier? Use add

$=1$ smoothing.

Part $4)$ How does a Naive Bayes classifier classify the review "movie of the year $."$ given the training data? Is this classification correct? Why has the classifier classified it this way?