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Suppose that Y₁, Y₂,..., Y, is a random sample from a probability density function in the (one-parameter) exponential family so that [a(0)b(y)e-le®)d(y)], a ≤ y ≤ b, f(y10) = 0, elsewhere, where a and b do not depend on 9. Show that Σd(Y) is sufficient for 0.

Suppose that Y₁, Y₂,..., Y, is a random sample from a probability density function in the (one-parameter) exponential family so that [a(0)b(y)e-le®)d(y)], a ≤ y ≤ b, f(y10) = 0, elsewhere, where a and b do not depend on 9. Show that Σd(Y) is sufficient for 0.

Calculus For The Life Sciences
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.
Chapter13: Probability And Calculus
Section13.1: Continuous Probability Models
Problem 16E
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Suppose that Y₁, Y₂,..., Y is a random sample from a probability density function in the (one-parameter) exponential family so that [a(0)b(y)e-[c(Ⓒ)d(y)], a ≤ y ≤ b, f(y10) = 0, elsewhere, where a and b do not depend on 9. Show that Σd(Y) is sufficient for 0.
Transcribed Image Text:Suppose that Y₁, Y₂,..., Y is a random sample from a probability density function in the (one-parameter) exponential family so that [a(0)b(y)e-[c(Ⓒ)d(y)], a ≤ y ≤ b, f(y10) = 0, elsewhere, where a and b do not depend on 9. Show that Σd(Y) is sufficient for 0.
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