Question: 3. Suppose that the random variable 8 takes the values 1J U and 1 with respective probabilities U4, 1/2 and U4. Suppose furthermore that given

3. Suppose that the random variable 8 takes the values 1J U and 1 with respective probabilities U4, 1/\"2 and U4. Suppose furthermore that given 8 = 8, the random variable X follows a normal {Gaussian} distribution with mean 8 and variance 1. {a} Show that the posterior distribution is given by (1+ 266+\"? + e23)_1 if e = 1 fags-m = 2 (e_3_1f2 + 2 + ex-1f2j'l '1er? = 0 (823 + 2e_$+1f2 + 1) '1 if e = 1. [5 marks] {b} Suppose that a sample X = x is observed. Find the Bayesian estimate for 6\" under the squared error loss function. [5 marks]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

please answer the following thank you so much for the help 1. What is the formula for the 2 points 3. What is the formula for the 2 points 6. The number of items sold 2 points 10. Find the variance...

1. Let X be a discrete random variable that may assume values x = 0; 1; 2 respectively with probabilities p1; 0:5; p2. Which values of p1 and p2 define a probability distribution? A p1 = 0.5 and p2 =...

\fPlease remember to start each question on a new page. 2. (6 points) Below are two improper integrals. If the integral is divergent, Show that it is divergent. If it is not divergent, evaluate it....

Hello i need this to be solved for me pls because i am preparing for exam at the moment and i dont know wat to do MAT 281 EXERCISES 1. Two students are randomly selected from a statistics class, and...

MAT 281 EXERCISES 1. Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. How many total outcomes are possible? Draw a tree...

Detailed answers. Problem 34.\" A spider and a y move along a straight line. At each second, the y moves a unit step to the right or to the left with equal probability p, and stays where it is with...

13. (3 points) Consider a scalar-valued random variable X that takes values {1,2,3,4} with probabilities Px(1) = 0.2, px (2) = 0.3, px(3) = 0.25, and px (4) = 0.25. Compute the mean and variance of...

Student: Sterling White Instructor: David Scott Date: 10/11/22 Course: Math 1324 PreCalculus for Business Assignment: Section 5.3 Homework 8. A manufacturing company makes two types of water skis. a...

1 (2 points) Which of the following statements are true? Question 1 options: Probabilities must be negative. Probabilities can either be positive or negative. Probabilities must be nonnegative....

What are economies of scale and diseconomies of scale? How do they arise? What do they imply for the shape of the LRAC curve?

Dark Skies Observatory is considering several options to purchase a new deep-space telescope. Revenue would be generated from the telescope by selling "time and use" slots to various researchers...

Which of the following is not one of the policies and procedures that make up an internal control system? Multiple Choice Profect assets Ensure reliable accoursing. Guarantee a return to irwestors....

2023 1040 form 1.Phillip and Claire are married and file a joint return. Phillip is self-employed as a real estate agent, and Claire is a flight attendant. Phillip and Claire have three dependent...