Suppose that a random sample is to be taken from a normal distribution for which the value of the mean is unknown and the standard deviation is 2, the prior distribution of is a normal distribution for which the standard deviation is 1, and the value of must be estimated by using the squared error loss function What is the smallest random sample that must be taken in order for the mean squared error of the Bayes estimator of to be 0 01 or less

Question: Suppose that a random sample is to be taken from a normal distribution for which the value of the mean is unknown and the

Suppose that a random sample is to be taken from a normal for which the value of the mean θ is unknown and the standard deviation is 2, the prior of θ is a normal for which the standard deviation is 1, and the value of θ must be estimated by using the squared error loss function. What is the smallest random sample that must be taken in order for the mean squared error of the Bayes estimator of θ to be 0.01 or less?

Step by Step Solution

★★★★★

3.40 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For any given values in the random sample the Bayes estimate ... 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

Document Format (1 attachment)

602-M-S-P-E (921).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Suppose that a random sample is to be taken from the normal distribution with unknown mean and standard deviation 2. How large a random sample must be taken in order that E (|n |2) 0.1 for every...

Suppose that a random sample is to be taken from the Bernoulli distribution with unknown parameter p. suppose also that it is believed that the value of p is in the neighborhood of 0.2. How large a...

Suppose that a random sample of size 1 is to be taken from a finite population of size N. a. How many possible samples are there? b. Identify the relationship between the possible sample means and...

Suppose that a random sample is to be taken from a normal distribution for which the value of the mean is unknown and the standard deviation is 2, and the prior distribution of is a normal...

I have questions about R programming. I am confused about question 5 and question 6, especially part d: 1 - pnorm(0.93, 0.932, 0.0448/sqrt(4)) [1] 0.5355726. I used standard deviation on question 4....

Suppose that you flip a coin 40 times and count the number of heads. 1.1. What is the distribution of the number of heads assuming the coin is fair? 1.2. The sample proportion of heads has an...

In a data set with 2500 points, the sample mean was calculated to be 3980, and the sample standard deviation was calculated to be 1000. Assuming that the data were generated from a random output that...

A study conducted by the technology company TiVo showed that the mean time spent per day browsing the video streaming service Netflix for something to watch was 19.5 minutes. Suppose a simple random...

Suppose that a random sample of 100 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in...

Which of the following statements is true with regards to globalization? 1. Creating a global marketing plan is no simple task. 2. Generating worldwide marketing plans requires most companiesto...

A previously issued A2, 15-year industrial bond provides a return three-fourths higher than the prime interest rate of 11 percent. Previously issued A2 public utility bonds provide a yield of...

4 (1 point) Saved Large-cap stocks had the nominal rates of return of 12.98 percent. The rate of inflation during the last year was 3.99 percent. What is the real rate of return for large-cap stocks

. YOU BE THE JUDGE WRITING PROBLEM Sarah went to an auction at Christies to bid on a tapestry for her employer, Fine Arts Gallery. The good news is that she purchased a Dufy tapestry for $77,000. The...

Each rear tire on an experimental airplane is supposed to be filled to a pressure of 40 pounds per square inch (psi). Let X denote the actual air pressure for the right tire and Y denote the actual...

Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X...

Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call....

j Alicia (age 27) is a single, full-time college student. She earns $13,200 from a part- time job and has taxable interest income of $1,450. Her itemized deductions are $845. Calculate Alicias...

The balance sheet for Ferguson Corp. is shown here in market value terms. There are 7,000 shares of stock outstanding. Instead of a dividend of $1.80 per share, the company has announced a share...

Question 4 Which of the following is not one of the three empirically observed facts related to the yield curve? Approximately half of the time the yield curve will slope up and half of the time it...