a)As we are going to classify , we need to calculate conditional probabilities for P(B=0|C=m), P(E=1|C=m), P(F=0|C=m), P(W=0.5|C=m), P(L=1|C=m).The same calculation needs to be done for C=b, C=a, C=r, and C=f.

If you cannot remember the formula for conditional probabilities, the following will help:

Let N(B=0, C=m) be the number of tuples having B=0 and C=m.

P(B=0|C=m) is N(B=0, C=m) / N(C=m)

P(B=0,E=1|C=m)= N(B=0, E=1, C=m) / N(C=m)

P(B=0|C=m,E=1)= N(B=0, E=1, C=m) / N(C=m,E=1)

b)Use the naive Bayes approach and the conditional probabilities calculated in (a) to predict the class label for the test tuple . Note that nave Bayesian assumes the independence among the input variables B,E,F,W, and L, thus

P(B=0,E=1,F=0,W=0.5,L=1|C=m)

= P(B=0|C=m)*P(E=1|C=m)*P(F=0|C=m)*P(W=0.5|C=m)*P(L=1|C=m)

The probability of the tuple having class m is

P(C=m | B=0,E=1,F=0,W=0.5,L=1)

= P(B=0,E=1,F=0,W=0.5,L=1|C=m)* P(C=m) / P(B=0,E=1,F=0,W=0.5,L=1)

c)Remove the correlated column E and use the nave Bayesian to do the classification again for the test tuple .

d)Compare b) and c) and explain whether the removal of E helps make the classification better or worse.

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