Suppose that X is a normal random variable with unknown mean and known variance 2 The prior distribution for is a uniform distribution defined over the interval a, b (a) Find the posterior distribution for (b) Find the Bayes estimator for

Question: Suppose that X is a normal random variable with unknown mean and known variance 2 . The prior distribution for is a

Suppose that X is a normal random variable with unknown mean μ and known variance σ². The prior distribution for μ is a uniform distribution defined over the interval [a, b].

(a) Find the posterior distribution for μ.

(b) Find the Bayes estimator for μ.

Step by Step Solution

★★★★★

3.52 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a the joint distribution is and this integral ... View full answer

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 Applied Statistics and Probability Questions!

Suppose that X is a normal random variable with unknown mean and known variance 2 = 9. The prior distribution for is normal with 0 = 4 and 2 0 = 1. A random sample of n = 25 observations is...

Suppose that X is a normal random variable with mean 5. If P{X > 9} = .2, approximately what is Var(X)?

If X is a normal random variable with mean 40 and standard deviation 10 and P(X > 45) = 0.3085, then P(X

Suppose that X is a normal random variable with unknown mean and known variance 2 . The prior distribution for is a normal distribution with mean 0 and variance . Show that the Bayes estimator for...

Suppose that X is a normal random variable with unknown mean and known variance 2 9. The prior distribution for is normal with 0 4 and 1. A random sample of n 25 observations is taken, and the...

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...

A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...

Consider data Y1,...,Yn that is a random (i.e. independent) sample from a Normal distribution with unknown mean and known variance 2 You wish to infer from the data using a Bayesian approach and...

12. Consider a population (a random variable X) with mean = 100 and variance 2 =900. The sample size = 30, so the central limit theorem applies. a) What are the mean and variance of the sampling...

here's my question 4. Blood pressure consists of two numbers, the systolic (upper) number and the diastolic (lower) number. Medical researches want to understand the difference in magnitude between a...

Seward Co. produces and sells restaurant equipment. On the first day of its fiscal year, Seward Co. issued $40,000,000 of five-year, 11% bonds at an effective interest rate of 14%, with interest...

The Year 2015 financial statements of the Russian subsidiary of Globe Corporation (a German company) revealed the following: Russian Ruble Beginning Inventory. $480,000 Purchases .... 360,000 Ending...

PROBLEM 10-6. Cash Budget In the fourth quarter of 2006, Casey Wholesalers had the following net income: Sales $500,000 Less cost of sales 250,000 Gross margin 250,000 Selling and administration...

18 What does the aggregate supply curve look like in the simple Keynesian model?

Use the complete-case method to relate lead levels in 1972 to full-scale IQ score (variable name IQF), while controlling for age and sex?

Repeat the analysis in Problem 13.77 using multipleimputation methods?

Compare your results in Problems 13.77 and 13.78?

An example of risk occurs when un investment does not keep up with prices that are increasing in the overall economy. A major cause of mortgage market meltdown in 2007 and 2008 was linked to What is...

Answer 22, 23, and 24 using the following information: Jane plans to open a new business. The equipment will cost $175,000. Jane expects the after-tax cash inflows to be $65,000 annually for 5 years,...

The primary difference between a line of credit and a revolving credit arrangement is the: a. length of the time period covered by the loan agreement b. type of collateral used to secure the loan c....