Consider a random sample X1,..., Xn from the population distribution with density f(x; 8) = 0x°-1, r € (0, 1), and parameter 0 e (0, 00). (1) Verify that the Assumptions (1) and (2) of the Cramér-Rao Theorem (Theorem 2.22) are met.

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A: the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0…

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A: The solution of the required question is as given in steps below.

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A: Since relationship is linear, hence Distribution of  Y = 50 + 3Z1 + 4Z2  is N(50, 25)

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A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

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A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

Q: (4) Let X be a discrete random variable with domain D. Prove that Var(X) = E(X?) – E(X).

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…