You will train a Naive Bayes classifier to predict class labels Y as a function of input features A and B$.$ Y $,$ A$,$ and B are all binary variables, with domains $0$ and $1.$ You are given $10$ training points from which you will estimate your distribution.

$($a$)$ What are the maximum likelihood estimates for the tables P$($Y $),$ P$($A$|$Y $),$ and P$($B$|$Y $)?$

$($b$)$ Consider a new data point $($A $=1,$ B $=0).$ What label would this classifier assign to this sample?

$($c$)$ Compute the new distribution for P$($A$|$Y$)$ using Laplace Smoothing with k $=2$ for smoothing out your distribution.