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#### Part II) Short Answer Solve each of the following problems

###### Math

Solve each of the following problems.

1. See the dataset below about Titanic passengers. Room is an independent variable representing the class of room passenger stayed in, first, second, and third. Survive is the dependent variable representing whether the passenger survived the accident. We wish to build a decision tree to determine whether a passenger survived, given room class. Please calculate the total entropy of the data, and the information gain once we use attribute Room as the root node of the decision tree.

 Room Survive 2nd Yes 1st No 3rd Yes 1st Yes 1st Yes 3rd No 2nd No 3rd No 1st Yes 3rd No 2nd Yes 3rd No

Note:

???!1 = 0, ???!

−1

???!

= −1.6, ???! 3 = −0.6

???! = −2,                 ???!

= −0.4

???! 5 = −2.3, ???! 5 = −1.3, ???!

= −0.7, ???!

= −0.3

1

1. See the neural network below, the values of each node in input layer xi are provided in the plot. All the weights for input layer and hidden layers, w1ij and w2ij, are given in the table below. Node x1 represents gender, where female is 1 and male is 0. Node x2 represents year of study, where freshman is 1, sophomore is 2, junior is 3, and senior is 4. Node x3 represents GPA. The output layer represents whether the student will get an A in the new course he/she is taking. Please use the neural network to predict whether a female sophomore student with a GPA of 3.0 will get an A in the course or not. Assume the neural network stops after one iteration of feedforward.

3

 Weight Weight w111 = 0.7 w211 = 0.9 w112 = 0.6 w212 = -0.9 w113 = 0.7 w221 = 0.8 w121 = 0.8 w222 = -0.8 w122 = 0.6 w231 = 0.7 w123 = 0.8 w232 = -0.7 w131 = 0.9 w132 = 0.4 w133 = 0.9

2

1. See the dataset below. There are four pieces of promotion and insurance information about customers used as evidence attributes: Flight Promotion, Magazine Promotion, Life Insurance, and Credit Insurance. Gender is the class variable. We wish to use Naïve Bayes to predict a customer’s gender, given the information about his/her promotion and insurance. Please find the conditional probability of

P(male | Flight Promotion=No, Magazine Promotion=Yes, Life Insurance=No, Credit Insurance=Yes).

 Flight Promotion Magazine Promotion Life Insurance Credit Insurance Gender Yes No No No Male Yes Yes Yes Yes Female No No No No Male Yes Yes Yes Yes Male Yes No Yes No Female No No No No Female Yes No Yes Yes Male No Yes No No Male Yes No No No Male Yes Yes Yes No Female

3

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