In the problems below we consider the following setup. Let X₁,..., Xn be independent copies of the random variable X where X is a mixture of two uniform random variables and has pdf: for some unknown > 0. For this problem, we call Unif([0, 20], the first component. First Initialization: EM for a Uniform Mixture Assume that n = 8 and the observations are 5. Mixture of Uniforms 0₁ ƒ (x) = 1 (x = [0, 20]) + 11 (x = [0,30)) 40 40 0₂ 03 Assume that the EM algorithm is initialized at 00 = 3. What are the values of the first three iterates 01, 02, and 03 of the EM algorithm? || X₁ = 1.01 X₂ = 1.02 X3 = 1.19 X₁ 1.19 X5 1.28 X6 = 2.39 X7 = 2.56 X = 2.58

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