A tech company is building a spam detection system using a Naive Bayes model that combines both Multinomial and Gaussian Naive Bayes. The dataset contains the following features:

Word Counts $($e$.$g$.,$ "Dear", "Friend", "Money"$)-$ Discrete. Time Between Messages $($in seconds$)-$ Continuous.

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Based on this dataset, answer the following:

$($a$)$ Explain why both Multinomial and Gaussian Naive Bayes are needed for this problem.

$($b$)$ Calculate the prior probabilities for the classes $($Spam and Not Spam$).$

$($c$)$ Given a new email with:

$$ Dear $=1,$ Friend $=1,$ Money $=0,$ Time Between Messages $=25$ sec

$$ Use a combination of Multinomial and Gaussian Naive Bayes to calculate the likelihood for this email being classified as Spam or Not Spam.

$($d$)$ Predict whether the new email is Spam or Not Spam based on the calculations.

$($e$)$ Discuss the importance of feature scaling for the continuous feature $($Time Between Messages$)$ in Gaussian Naive Bayes