This assignment is related to the simulation study described in Section 2.3.1 (the so-called Scenario 2 or Example 2) of "Elements of Statistical Learning" (ESL). Scenario 2: the two-dimensional data X R2 in each class are generated from a mixture of 10 different bivariate Gaussian distributions with uncorrelated components and different means, i.e., X | Y = k, Z = j N (mkj , s2 I2) where k = 0, 1, and j = 1, 2, . . . , 10. Set P(Y = k) = 1/2, P(Z = j) = 1/10, s2 = 1/5. In other words, given Y = k, X follows a mixture distribution with probability density function (PDF) 1 10 X 10 j=1 1 2s2 2 e kxmkj k 2/(2s 2 ) . Part 1: Generate Data 1. First generate the 20 centers from two-dimensional normal and randomly split them into two classes of 10. You can use any mean and covariance structure. You should not regenerate the centers. Use these 20 centers throughout this simulation study. 2. Given the 20 centers, generate a training sample of size 200 (100 from each class) and a test sample of size 10,000 (5,000 from each class). 3. Produce a scatter plot of the training data: assign different colors to the two classes of data points; overlay the 20 centers on this scatter plot, using a distinguishing marker (e.g., a star or a different shape) and color them according to their respective class