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Let X₁,..., X5 be a random sample from a Bernoulli distribution with parameter p and let the prior distribution have a Beta distribution with the pdf f(x; a) = 6x(1x) for 0

Let X₁,..., X5 be a random sample from a Bernoulli distribution with parameter p and let the prior distribution have a Beta distribution with the pdf f(x; a) = 6x(1x) for 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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- Let X₁,..., X5 be a random sample from a Bernoulli distribution with parameter p and let the prior distribution have a Beta distribution with the pdf f(x; a) = 6x(1 — x) for 0<x< 1, and zero otherwise. If the sum of the observed sample is 3 (i.e., ₁ ; = 3), which statement is correct? (1) The posterior distribution has a Beta distribution with parameters 4 and 3 respectively. (II) The posterior distribution has a Beta distribution with parameters 3 and 4 respectively. (III) The posterior distribution has a Beta distribution with parameters 5 and 4 respectively. (IV) The posterior distribution has a Beta distribution with parameters 4 and 5 respectively. O (III) O (II) O (IV) O (1)
Transcribed Image Text:- Let X₁,..., X5 be a random sample from a Bernoulli distribution with parameter p and let the prior distribution have a Beta distribution with the pdf f(x; a) = 6x(1 — x) for 0<x< 1, and zero otherwise. If the sum of the observed sample is 3 (i.e., ₁ ; = 3), which statement is correct? (1) The posterior distribution has a Beta distribution with parameters 4 and 3 respectively. (II) The posterior distribution has a Beta distribution with parameters 3 and 4 respectively. (III) The posterior distribution has a Beta distribution with parameters 5 and 4 respectively. (IV) The posterior distribution has a Beta distribution with parameters 4 and 5 respectively. O (III) O (II) O (IV) O (1)
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