Let (x1, x2,,n) be i.i.d. samples a random variable Xwith the following probability density function:fx(x) = {10if 0 < x < 0+1otherwise,where > 0 is unknown. In an experiment, the following observations/sampleswere 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 onthe 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 simulatedobservation U.

Answered: Let (x1,x2,. ,n) be i.i.d. samples a…

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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Related questions

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.

Expert Solution

Step 1: Write the given information

Given that $open parentheses x subscript 1 comma space x subscript 2 comma space times space times space times comma space x subscript n close parentheses$ be i.i.d. samples a random variable X with the following probability density function:

$f subscript X open parentheses x close parentheses equals open curly brackets table row cell 1 space space space i f space theta less than x less or equal than theta plus 1 end cell row cell 0 space space space o t h e r w i s e end cell end table close$

where $theta greater than 0$ is unknown.