Homework Help is Here – Start Your Trial Now!
Math
Statistics
nally distributed with mean 0 and a known variance 4, so the value z th is modeled by N(0,4). Based on previous communications, your prior or e your friend transmits a value to you that you receive as x6. Show th sterior pdf foris N(74/13, 36/13). For this problem, you need to deri sterior by carrying out the calculations from scratch. e your friend transmits the same value to you n = 4 times. You rece ignals plus noise as ₁,..., with sample mean = 6. Using the same pr own variance o² as in part (a), show that the posterior on 0 is N(5.9,0.1 e posterior and posterior on the same graph. Describe how the data chang

nally distributed with mean 0 and a known variance 4, so the value z th is modeled by N(0,4). Based on previous communications, your prior or e your friend transmits a value to you that you receive as x6. Show th sterior pdf foris N(74/13, 36/13). For this problem, you need to deri sterior by carrying out the calculations from scratch. e your friend transmits the same value to you n = 4 times. You rece ignals plus noise as ₁,..., with sample mean = 6. Using the same pr own variance o² as in part (a), show that the posterior on 0 is N(5.9,0.1 e posterior and posterior on the same graph. Describe how the data chang

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

a) & b)

Your friend transmits an unknown value to you over a noisy channel. The noise is normally distributed with mean 0 and a known variance 4, so the value x that you receive is modeled by N(0,4). Based on previous communications, your prior on is N (5,9). (a) Suppose your friend transmits a value to you that you receive as x = 6. Show that the posterior pdf foris N(74/13, 36/13). For this problem, you need to derive the posterior by carrying out the calculations from scratch. (b) Suppose your friend transmits the same value to you n = 4 times. You receive these signals plus noise as ₁,..., with sample mean = 6. Using the same prior and known variance o² as in part (a), show that the posterior on 0 is N(5.9,0.9). Plot the posterior and posterior on the same graph. Describe how the data changes your belief about the true value of 0. For this question, you may use the normal updating formulas.
Transcribed Image Text:Your friend transmits an unknown value to you over a noisy channel. The noise is normally distributed with mean 0 and a known variance 4, so the value x that you receive is modeled by N(0,4). Based on previous communications, your prior on is N (5,9). (a) Suppose your friend transmits a value to you that you receive as x = 6. Show that the posterior pdf foris N(74/13, 36/13). For this problem, you need to derive the posterior by carrying out the calculations from scratch. (b) Suppose your friend transmits the same value to you n = 4 times. You receive these signals plus noise as ₁,..., with sample mean = 6. Using the same prior and known variance o² as in part (a), show that the posterior on 0 is N(5.9,0.9). Plot the posterior and posterior on the same graph. Describe how the data changes your belief about the true value of 0. For this question, you may use the normal updating formulas.
Expert Solution
steps

Step by step

Solved in 5 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS