Consider the following events: A: X₁, X2,..., Xn are independent and come from a Rayleigh distribution with pdf fi(x) = — exp(-25) on x > 0. • A: X1, X2,..., Xn are independent and come from an exponential distribution with pdf f2(x) = 02 exp(-0₂x) on x > 0. (a) Show that the Bayes factor, B(x, A), for event A against event Aº is exp(62 Σr - B(x, A) = I1¹₁ o en 201

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.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
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Consider the following events:
A: X1, X2, ...,X, are independent and come from a Rayleigh
distribution with pdf
fi(x) =
- exp
on r> 0.
01
201
A° : X1, X2,.., Xn are independent and come from an exponential
distribution with pdf
f2(x) = 02 exp (-02x)
on r> 0.
(a) Show that the Bayes factor, B(x, A), for event A against event A is
B(r, A) =
exp ( 02 > ri
201
Transcribed Image Text:Consider the following events: A: X1, X2, ...,X, are independent and come from a Rayleigh distribution with pdf fi(x) = - exp on r> 0. 01 201 A° : X1, X2,.., Xn are independent and come from an exponential distribution with pdf f2(x) = 02 exp (-02x) on r> 0. (a) Show that the Bayes factor, B(x, A), for event A against event A is B(r, A) = exp ( 02 > ri 201
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