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Suppose data are positive numbers z1, T2, … .., T, and suppose it is decided to model these by i.i.d. random variables X1, X2,..., X, with common Gamma(v, A) distribution as described in Definition 3.12 of the notes. Here the shape parameter v is supposed to be known, but the rate parameter A € (0, 0) is unknown and needs to be estimated. Let A be the MLE for A. Setting i = Ti, which of the following statements is true? O î = 7/v. O If Z is defined by substituting X, for ¤; in A then Z1 has a Gamma(nv, A) distribution. O If Z is defined by substituting X; for z; in A then Z-1 has a Gamma(nv, nvd) distribution. O If Z is defined by substituting X; for ; in A then Z has a Gamma(nv, A/(nv)) distribution.

Suppose data are positive numbers z1, T2, … .., T, and suppose it is decided to model these by i.i.d. random variables X1, X2,..., X, with common Gamma(v, A) distribution as described in Definition 3.12 of the notes. Here the shape parameter v is supposed to be known, but the rate parameter A € (0, 0) is unknown and needs to be estimated. Let A be the MLE for A. Setting i = Ti, which of the following statements is true? O î = 7/v. O If Z is defined by substituting X, for ¤; in A then Z1 has a Gamma(nv, A) distribution. O If Z is defined by substituting X; for z; in A then Z-1 has a Gamma(nv, nvd) distribution. O If Z is defined by substituting X; for ; in A then Z has a Gamma(nv, A/(nv)) distribution.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Suppose data are positive numbers a1, 2, . .., T, and suppose it is decided to model these by i.i.d. random variables X1, X2, ..., X, with common Gamma(v, A) distribution as described in Definition 3.12 of the notes. Here the shape parameter v is supposed to be known, but the rate parameterdE (0, 00) is unknown and needs to be estimated. Let Å be the MLE for A. Setting i = , e;, which of the following statements is true? O i=7/v. O If Z is defined by substituting X; for æ; in A, then Z1 has a Gamma(nv, A) distribution. O If Z is defined by substituting X; for a; in Ä, then Z-1 has a Gamma(nv, nvd) distribution. O If Z is defined by substituting X; for æ; in A, then Z has a Gamma(nv, A/(nv)) distribution. O Â=v/T. O î = (2)". O If Z is defined by substituting X; for æ; in A, then Z has a Gamma(nv, X) distribution.
Transcribed Image Text:Suppose data are positive numbers a1, 2, . .., T, and suppose it is decided to model these by i.i.d. random variables X1, X2, ..., X, with common Gamma(v, A) distribution as described in Definition 3.12 of the notes. Here the shape parameter v is supposed to be known, but the rate parameterdE (0, 00) is unknown and needs to be estimated. Let Å be the MLE for A. Setting i = , e;, which of the following statements is true? O i=7/v. O If Z is defined by substituting X; for æ; in A, then Z1 has a Gamma(nv, A) distribution. O If Z is defined by substituting X; for a; in Ä, then Z-1 has a Gamma(nv, nvd) distribution. O If Z is defined by substituting X; for æ; in A, then Z has a Gamma(nv, A/(nv)) distribution. O Â=v/T. O î = (2)". O If Z is defined by substituting X; for æ; in A, then Z has a Gamma(nv, X) distribution.
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