Mean and Variance of a Mixture Recall that X follows a mixture of two Gaussians if and only if X = ZX1 + (1 – Z) X2 where Z ~ Ber (1), X1 ~ N (41,0}), X2 ~ N (42, 03) and Z is independent of X1 and X2. Assume that 41 = 0, 42 = 1 and of = o =1 and T = 1/4. Note that r here is not the constant 3.14... What is the expected value of X? E [X] = What is the variance of X? Var (X) = For the above computations, do you have to assume that X1 is independent of X2? Yes No

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A: The provided information is as follows:. and  are independent random variables..

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A: We will calculate one by one in the following manner from the given data:

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A: Given Data: E(X)=6 E[(X) (X-1)]=51

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A: The joint pmf for X and Y is given in the accompanying table

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A: Solution

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