Consider the dataset shown in Table 3.
Instance
A
B
C
Class
1
0
0
1
-
2
1
0
1
+
3
0
1
0
-
4
1
0
0
-
5
1
0
1
+
6
0
0
1
+
7
1
1
0
-
8
0
0
0
-
9
0
1
0
+
10
1
1
1
+
Table 3
a. [3 points] Estimate the conditional probabilities for $P(A = 1|+)$, $P(B = 1|+)$, $P(C = 1|+)$, $P(A = 1|-)$, $P(B = 1|-)$, and $P(C = 1|-)$.
b. [2 points] Use the conditional probabilities in part (a) to predict the class label for a test sample $(A = 1, B = 1, C = 1)$ using the naïve Bayes approach.
c. [2 points] Compare $P(A = 1, B = 1 | Class = +)$ against $P(A = 1 | Class = +)$ and $P(B = 1 | Class = +)$. Are the variables conditionally independent given the class?
