For classifying a new sample into four classes: C1, C2, C3, and C4, we have an ensemble that consists of three different classifiers: Classifier 1, Classifiers 2, and Classifier 3. Each of them has 0.9, 0.6, and 0.6 accuracy rate on training samples, respectively. When the new sample, X, is given, the outputs of the three classifiers are as follows:

Class Label	Classifier 1	Classifier 2	Classifier 3
C1	0.9	0.3	0
C2	0	0.4	0.9
C3	0.1	0.2	0
C4	0	0.1	0.1

Each number in the above table describes the probability that a classifier predicts the class of a new sample as a corresponding class. For example, the probability that Classifier 1 predicts the class of X as C1 is 0.9.

When the ensemble combines predictions of each of them, as a combination method:

*** I'M INTERESTED IN THE MATH, NOT THE CODE ***

If the simple sum is used, which class is X classified as and why?

If the weight sum is used, which class is X classified as and why?

If the ran-level function is used, which class if X classified as and why?