In the subproblems below, X is a mixed distribution with k components X_k, with respective weights w_k. For each subproblem, find μ_X, Var(X), and P(X ≥ 0).

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(a) 2 components. W = 0.2, w = 0.8. = -3, = 5, Var(X) = 9, Var(X2)=16, P(X 0) = 0.2, P(X 0) = 0.9. (b) 2 components. W = 0.9, Var(X2)=50, P(X 0) = (c) 2 components. W = 0.5, Var(X2)=25, P(X 0) = (d) 3 components. W = 0.1, w2 = 0.1. = 7, = 11, Var(X1) = 50, 0.11, P(X2 > 0) = 0.11. w = 0.5. = 5, = -5, Var(X) = 25, 1, P(X2 0) = 0. M3 w = 0.6, w3 = 0.3. = 2, M = 4, 3 = 8, Var(X1)=4, Var(X2)=8, Var(X3) = 16, P(X 0) = 0.841 345, P(X220) 0.921 35, P(X3 > 0) = 0.977 25. (e) 3 components. W = 0.9, w = 0.09, w3 = 0.01. = 1, = 2, 3 = 100, Var(X1) = 1, Var(X2) = 1, Var(X3) = 1, P(X 0) = 0.841 345, P(X20) = 0.977 25, P(X3 0) = 1.