In class, we learned a Nave Bayes classi er for binary feature values, i. e., xj 2 f0; 1g where we model the class conditional distribution to be Bernoulli. In this exercise, you are going to extend the result to the case where features that are non-binary. We are given a training set f(x(i); y(i)); i = f1; ;mgg, where x(i) 2 f1; 2; ; sgn and y(i) 2 f0; 1g. Again, we model the label as a biased coin with 0 = P(y(i) = 0) and 1 0 = P(y(i) = 1). We model each non-binary feature value x(i) j (an element of x(i)) as a biased dice for each class. This is parameterized by:
P(zj-s|y = 1) = θ.sly=1
Notice that we do not model P(aj sly = 0) and Pu; = sly = 1) directly. Instead we use the above equations to guarantee all probabilities for each class sum to 1.
A) Using the Naive Bayes (NB) assumption, write down the joint probability of the data: in terms of the parameters θο, θjkly-0 and ,,k y-1. You mlay find the indicator function 1(-) useful.
B) Maximizing the joint probability you get in (a) with respect to o, ,ky-o and jk y-1. Write down your resulting θο, θ, k y 0 and θ.kl,-1 and show intermediate steps.

7.23 main lab 7 - online shopping cart background this main lab extends the earlier prep lab "online shopping cart part 1". (you should save this as a separate project from the earlier prep lab). you will create an on-line shopping cart like you might use for your on-line purchases. the goal is to become comfortable with setting up classes and using objects. requirements this lab can be done individually or as pair programming. expanded itemtopurchase class (15 points) extend the itemtopurchase class as follows. we will not do unit testing in this lab so we will not be giving you the names of the member functions. create good ones on your own. create a parameterized constructor to assign item name, item description, item price, and item quantity (default values of "none" for name and description, and 0 for price and quantity). additional public member functions set an item description get an item description print the cost of an item - outputs the item name followed by the quantity, price, and subtotal (see example) print the description of an item - outputs the item name and description (see example) additional private data members a string for the description of the item. example output of the function which prints the cost of an item: bottled water 10 @ $1.50 = $15.00 example output of the function which prints the item description: