Prove that if the family of the density functions for U is complete, g 1 ( U ) must equal g 2 ( U ) , and thus there is a unique function of U that is an unbiased estimator of θ .

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Answer 1

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Chapter 9.5, Problem 68E

To determine

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

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4. Let X, Y be non-negative continuous random variables with probability density functions (pdf) gx(x) and gy (y), respectively. Further, let f(x, y) denote their joint pdf. We say that X and Y are independent if f(x, y) = 9x(x)hy (y) for all x, y ≥ 0. Further, we define the expectation of X to be E[X] = √rg(x)dx, to be the expectation of XY. 0 with a similar definition for Y but g replaced by h and x replaced by y. We also define E[XY] = (0,00)x (0,00) 110,00)x (0,00) 29 (x, y) dedy (0,∞) Use Fubini's theorem (which you may assume holds) to show that if X and Y are independent, then E[XY] = E[X]E[Y]. [2]

4. Let X, Y be non-negative continuous random variables with probability density functions (pdf) gx(x) and gy (y), respectively. Further, let f(x, y) denote their joint pdf. We say that X and Y are independent if f(x, y) = gx (x)hy (y) for all x, y ≥ 0. Further, we define the expectation of X to be - 1.²0⁰ with a similar definition for Y but g replaced by h and x replaced by y. We also define to be the expectation of XY. E[X] = xg(x) dx, E(XY)= (0,00)x(0,00) Tuf(x,y)dady (0,∞) (0,∞) Use Fubini's theorem (which you may assume holds) to show that if X and Y are independent, then E[XY] = E[X]E[Y].

Let X₁, X2, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = (0, -, if 0

Answer 2

Question

Chapter 9.5, Problem 68E

To determine

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

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Answer 3

Question

Chapter 9.5, Problem 68E

To determine

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

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Answer 4

Question

Chapter 9.5, Problem 68E

To determine

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

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Answer 5

Chapter 9.5, Problem 68E

To determine

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

Answer 6

Chapter 9.5, Problem 68E

To determine

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

Answer 7

Chapter 9.5, Problem 68E

To determine

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

Answer 8

Expert Solution & Answer

Answer 9

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Answer 10

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Answer 11

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Prove that if the family of the density functions for U is complete, g 1 ( U ) must equal g 2 ( U ) , and thus there is a unique function of U that is an unbiased estimator of θ .

Solution Summary: The author demonstrates that if the family of density functions for U is complete, there is a unique function of U that is an unbiased estimator of.

Prove that if the family of the density functions for U is complete, g1(U) must equal g2(U), and thus there is a unique function of U that is an unbiased estimator of θ.

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