11. Suppose that we are applying EM to data items each consisting of a single real value, x, using k=2 Gaussian clusters. We have N = 4 training cases, in which the values of x are as follows: 5, 10, 20, 30 for i=1 ... 4 We use the EM algorithm to find the maximum likelihood estimates for the model parameters, which are the probabilities of each cluster, al and 72, and the means for the two clusters, ul and u2. The standard deviations for the two components are fixed at 10. Suppose that at some point in the EM algorithm, the expectation step found that the responsibilities of the two clusters for the five data items were as follows: i ril ri2 1 0.6 0.4 2 0.3 0.7 3 0.7 0.3 4 0.9 0.1 Note: the EM-algorithm equations (from Assignment 2) will be provided on the exam. What value of nl and 12 will be found in the next maximization step of the algorithm? What value of ul and u2 will be found in the next maximization step of the algorithm? 11. Suppose that we are applying EM to data items each consisting of a single real value, x, using k=2 Gaussian clusters. We have N = 4 training cases, in which the values of x are as follows: 5, 10, 20, 30 for i=1 ... 4 We use the EM algorithm to find the maximum likelihood estimates for the model parameters, which are the probabilities of each cluster, al and 72, and the means for the two clusters, ul and u2. The standard deviations for the two components are fixed at 10. Suppose that at some point in the EM algorithm, the expectation step found that the responsibilities of the two clusters for the five data items were as follows: i ril ri2 1 0.6 0.4 2 0.3 0.7 3 0.7 0.3 4 0.9 0.1 Note: the EM-algorithm equations (from Assignment 2) will be provided on the exam. What value of nl and 12 will be found in the next maximization step of the algorithm? What value of ul and u2 will be found in the next maximization step of the algorithm