Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0) 0, 0 1, where 0 > 0 is unknown. Let 1 -да-1 еxp(-0) r(a) f(0) be the prior distribution for 0, where a > 0 is a known constant, r(:) is the gamma function defined as I(a) = S xa-le¬" dx for a > 0.
Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0) 0, 0 1, where 0 > 0 is unknown. Let 1 -да-1 еxp(-0) r(a) f(0) be the prior distribution for 0, where a > 0 is a known constant, r(:) is the gamma function defined as I(a) = S xa-le¬" dx for a > 0.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question

Transcribed Image Text:Find the posterior
mean for 0. Hint: If Y ~ Gamma(a, B), then E(Y)= a/ß.

Transcribed Image Text:Let X1,..., Xn be a random sample from a population with probability density function (pdf)
f(x | 0) = { Ox°, 0<x< 1,
0,
x < 0 or x > 1,
where 0 > 0 is unknown. Let
1
-0о-1 еxp(-0)
Г(о)
f(0) =
be the prior distribution for 0, where a > 0 is a known constant, I'(-) is the gamma function
defined as r(a) = S xª-'e°
dx for a > 0.
Expert Solution

Step 1
We have given that
Then we have to find the posterior distribution of theta:
Step by step
Solved in 3 steps with 3 images
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