Let (x1,x2,. ,n) be i.i.d. samples a random variable X with the following probability density function: √ 1 if 0 < x≤ 0+1 0 otherwise, fx(x) = { where > 0 is unknown. In an experiment, the following observations/samples were obtained from the above distribution. x₁ = 0.3, x₂ = 0.4, x3 = 0.2, x4 = 1.0, x5 = 0.9 (a) Find the posterior distribution of for the given data set based on the following prior distribution on 0: π(0) = 0.5e-101 (b) Show how you will simulate an observation from the posterior distri- bution in (a) assuming you can only simulate U from a Uniform([0, 1]) distribution. Give the explicit function relating to the simulated observation U.
Let (x1,x2,. ,n) be i.i.d. samples a random variable X with the following probability density function: √ 1 if 0 < x≤ 0+1 0 otherwise, fx(x) = { where > 0 is unknown. In an experiment, the following observations/samples were obtained from the above distribution. x₁ = 0.3, x₂ = 0.4, x3 = 0.2, x4 = 1.0, x5 = 0.9 (a) Find the posterior distribution of for the given data set based on the following prior distribution on 0: π(0) = 0.5e-101 (b) Show how you will simulate an observation from the posterior distri- bution in (a) assuming you can only simulate U from a Uniform([0, 1]) distribution. Give the explicit function relating to the simulated observation U.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![Let (x1, x2,,n) be i.i.d. samples a random variable X
with the following probability density function:
fx(x) = {
1
0
if 0 < x < 0+1
otherwise,
where > 0 is unknown. In an experiment, the following observations/samples
were obtained from the above distribution.
x₁ = 0.3, x₂ = 0.4, x3 = 0.2, x4 = 1.0, x5
= 0.9
(a) Find the posterior distribution of for the given data set based on
the following prior distribution on 0:
π(0) = 0.5e-101
(b) Show how you will simulate an observation from the posterior distri-
bution in (a) assuming you can only simulate U from a Uniform([0, 1])
distribution. Give the explicit function relating to the simulated
observation U.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea47a4b1-a227-4b18-bcf9-7f7b72a7a749%2F686af655-9808-48f3-8a96-42c209d7d41b%2Foc5a2kl_processed.png&w=3840&q=75)
Transcribed Image Text:Let (x1, x2,,n) be i.i.d. samples a random variable X
with the following probability density function:
fx(x) = {
1
0
if 0 < x < 0+1
otherwise,
where > 0 is unknown. In an experiment, the following observations/samples
were obtained from the above distribution.
x₁ = 0.3, x₂ = 0.4, x3 = 0.2, x4 = 1.0, x5
= 0.9
(a) Find the posterior distribution of for the given data set based on
the following prior distribution on 0:
π(0) = 0.5e-101
(b) Show how you will simulate an observation from the posterior distri-
bution in (a) assuming you can only simulate U from a Uniform([0, 1])
distribution. Give the explicit function relating to the simulated
observation U.
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