1. Consider an array of real values as shown below X-[11.55,11.07,13.31,10.92,11.89,13.63, 66.46, 73.38, 75.38, 73.01, 69.44,...

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1. Consider an array of real values as shown below X-[11.55,11.07,13.31,10.92,11.89,13.63, 66.46, 73.38, 75.38, 73.01, 69.44, 68.58]. Assume that the random values are drawn from the two groups A and B with Gaussian distribution. Each group has prior probability of 0.5. Perform the Expectation-Maximization algorithm on the given data. At the initial step, the A group has formed with Gaussian distribution with mean 2.0 and standard deviation 1.5, and second group B has mean 7.0 and standard deviation 2.0. Show all the steps for Expectation-Maximization on the give sample data for two iterations. Show the computed values such as likelihood for any sample x,, posterior probability, mean, and variance for each group. [6] 1. Consider an array of real values as shown below X-[11.55,11.07,13.31,10.92,11.89,13.63, 66.46, 73.38, 75.38, 73.01, 69.44, 68.58]. Assume that the random values are drawn from the two groups A and B with Gaussian distribution. Each group has prior probability of 0.5. Perform the Expectation-Maximization algorithm on the given data. At the initial step, the A group has formed with Gaussian distribution with mean 2.0 and standard deviation 1.5, and second group B has mean 7.0 and standard deviation 2.0. Show all the steps for Expectation-Maximization on the give sample data for two iterations. Show the computed values such as likelihood for any sample x,, posterior probability, mean, and variance for each group. [6]