Problem #3 [10 points] In a 5-class classification problem, 30 training examples are supplied that have the following class labels: 3 1 2 2 5 5 3 3 5 3 5 3 2 5 5 5 3 5 1 3 3 5 5 3 5 2 2 1 5 2 From the training data, we wish to estimate the probabilities of each class. Empirically estimate each class probability using (a) relative frequency, (b) Laplace correction, (C) m- estimate with m=5 and an even distribution of the pseudocounts, and (d) m-estimate with m=20 and an even distribution of the pseudocounts. Plot these empirical probabilities, with class number on the x-axis and estimated probability on the y-axis i.e., four plots (one for each approach), each of which consists of five connected points (the estimated class probabilities). Plot all four distributions on a single graph and label them. Describe the trend as we go from (a) to (b) to (C) to (d) that is, what does increasing the number of pseudocounts do (in general) to the probability distribution? Problem #3 [10 points] In a 5-class classification problem, 30 training examples are supplied that have the following class labels: 3 1 2 2 5 5 3 3 5 3 5 3 2 5 5 5 3 5 1 3 3 5 5 3 5 2 2 1 5 2 From the training data, we wish to estimate the probabilities of each class. Empirically estimate each class probability using (a) relative frequency, (b) Laplace correction, (C) m- estimate with m=5 and an even distribution of the pseudocounts, and (d) m-estimate with m=20 and an even distribution of the pseudocounts. Plot these empirical probabilities, with class number on the x-axis and estimated probability on the y-axis i.e., four plots (one for each approach), each of which consists of five connected points (the estimated class probabilities). Plot all four distributions on a single graph and label them. Describe the trend as we go from (a) to (b) to (C) to (d) that is, what does increasing the number of pseudocounts do (in general) to the probability distribution