((C) (; {)) Consider the family of bivariate normal distributions, N2 (a) Does the model belong to the exponential family of distributions? (b) Find the minimal sufficient statistic for p; (c) Prove that the model belongs to a curved 2-parameter exponential family of distributions;

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
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8. Consider the family of bivariate normal distributions, N2
(a) Does the model belong to the exponential family of distributions?
(b) Find the minimal sufficient statistic for p;
(c) Prove that the model belongs to a curved 2-parameter exponential family of distributions;
(d) Find the natural parameters of the model.
Transcribed Image Text:* ((:) (; ;)) 8. Consider the family of bivariate normal distributions, N2 (a) Does the model belong to the exponential family of distributions? (b) Find the minimal sufficient statistic for p; (c) Prove that the model belongs to a curved 2-parameter exponential family of distributions; (d) Find the natural parameters of the model.
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