our predicted claBayes' theorem is widely used in machine learning applications that include classification-based problems, in order to calculate conditional probabilities. It contributes to more accurate results. Suppose that the manager of a mobile network operator has information about his customers' age, income, occupation and credit rating, as given in Table 1. He wants to predict whether a young customer, who is a student, with medium income and a fair credit rating will or will not buy a mobile network subscription. Table 1 Dataset from the mobile network operator. Age Income Student Credit rating Buys subscription young high no fair no young high no excellent no middle aged high no fair yes senior medium no fair yes senior low yes fair yes senior low yes excellent no middle aged low yes excellent yes young medium no fair no young low yes fair yes senior medium yes fair yes young medium yes excellent yes middle aged medium no excellent yes middle aged high yes fair yes senior medium no excellent no Assume that buying subscription has two classes CY and CN, considering that both classes are equally likely. Let the event B be defined as {age = young, student = yes, income = medium, credit rating = fair}, where we consider these attribute's values to be independent of one another conditionally: ( | ) = (1 | ) (2 | ) ... ( | ). The goal of this project is to learn how to apply a Bayes classifier to predict whether = { = , = , = , = } belongs to class CY or CN. The class delivering the highest posterior probability will be chosen as the best class. Thus, we need to use Bayes' theorem for each class C, and our predicted class will be the class achieving the highest Course Title: Probabilistic Methods for Electrical and Computer Engineering Course Code: CE/EE-302 | 3 probability ( | ) (). So, to maximize ( | ), we need to maximize [ ( | ) () ] = = . Such a classification algorithm is called the Naive Bayes Classifier, which is a "simplified version" of the Bayes' theorem, and it is used to classify data into various classes with accuracy and speed. a) Using Table 1, find the probability ( = ), and find the probability ( = ). [10 points] b) Using Table 1, find how subscription sales are distributed across three age-classes of customers young (18-35), middle-aged (35-60), and seniors (60+). [15 points] c) Find the joint probabilities for age and income and show that the properties of joint PMF are satisfied. Calculate also the marginal PMF of age and the marginal PMF of income. Finally, find the expected number of customers in the age categories. [15 points] d) Using Table 1, find the following conditional probabilities: ( = | = ), ( = | = ), ( = | = ), ( = | = ). [15 points] e) Using Table 1, find the following conditional probabilities: ( = | = ), ( = | = ), ( = | = ), ( = | = ). [15 points] f) Find the probability ( | = ) and find the probability ( | = ). [10 points] g) Predict whether a young customer, who is a student, with medium income and a fair credit rating will or will not buy a mobile network subscription. [ss will be the class achieving the highest