You plan to use a rod to lay out a square, each side of which is the length of the rod The length of the rod is , which is unknown You are interested in estimating the area of the square, which is 2 Because is unknown, you measure it n times, obtaining observations X 1 , X 2 , , X n Suppose that each measurement is unbiased for with variance 2 (a) Show that X 2 is a biased estimate of the area of the square (b) Suggest an estimator that is unbiased

Question: You plan to use a rod to lay out a square, each side of which is the length of the rod. The length of the

You plan to use a rod to lay out a square, each side of which is the length of the rod. The length of the rod is μ, which is unknown. You are interested in estimating the area of the square, which is μ². Because μ is unknown, you measure it n times, obtaining observations X₁, X₂, …., X_n. Suppose that each measurement is unbiased for μ with variance σ².

(a) Show that X̅² is a biased estimate of the area of the square.

(b) Suggest an estimator that is unbiased.

Step by Step Solution

★★★★★

3.46 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Therefore X 2 is bia... 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!

In Exercises 1, assume that you plan to use a significance level of a - 0.05 to test the claim that p1.= p2. Use the given sample sizes and numbers of successes to find (a) The pooled estimate p-,...

In Exercises 2, assume that you plan to use a significance level of a - 0.05 to test the claim that p1. = p2. Use the given sample sizes and numbers of successes to find (a) The pooled estimate p-,...

You are planning a multiple linear regression analysis to predict profitability for companies in the region. One of the variables type of company is categorical. You plan to use dummy variables to...

You plan to use a rod to lay out a square, each side of which is the length of the rod. The length of the rod is , which is unknown. You are interested in estimating the area of the square, which is...

Using a long rod that has length m, you are going to lay out a square plot in which the length of each side is m. Thus the area of the plot will be 2. However, you do not know the value of m, so you...

1. Using a long rod that has length , you are going to lay out a square plot in which the length of each side is . Thus the area of the plot will be u". However, you do not know the value of u, so...

10. Using a long rod that has length m, you are going to lay out a square plot in which the length of each side is m. Thus the area of the plot will be m2. However, you do not know the value of m, so...

0 Using a long rod that has length you are going to lay out a square plot in which the length of each side is p Thus the area of the plot will be However you do not know the value of p so you decide...

10. Using a long rod that has length , you are going to lay out a square plot in which the length of each side is . Thus the area of the plot will be 2 . However, you do not know the value of , so...

The first question: Each student must choose a company listed on the Saudi Stock Exchange Tadawul- (other than the financial sector) and upload it financially (income statement and financial...

Data for Rajesh Company are presented in P13-7A. Further analysis reveals the following. 1. Accounts payable pertain to merchandise suppliers. 2. All operating expenses except for depreciation were...

9. Employee Retention. Employee retention is a major concern for many companies. A survey of Americans asked how long they have worked for their current employer (Bureau of Labor Statistics website)....

9 Explain the multiplier process.

Estimate the OR between widowhood and mortality, and provide a 95% CI about this estimate? Mental Health Refer to Table 10.27. Table 13.27 Use of SAS PROC PHREG to perform conditional logistic...

1. Use logistic regression methods to assess whether there is an association between ovarian cancer risk and duration of OC use while controlling for age. Provide a two-sided p-value. Assume that the...

What is the attributable risk (AR) of high BMI (¥25) for progression of AMD? Ophthalmology The data in Table 13.59 were presented relating body mass index (BMI) to progression of advanced...

For the two projects below, determine the acceptable projects based on the following: coe Payback Period cae Discounted Payback coe Net Present Value coe Profitability Index (Benefit-Cost Ratio) cse...

1. want determine if there is a significant correlation between cumulative GPA and having access to free meals at 7 Ontario universities. We tabulate the data as follows (see the table on the next...

Specify how risk aversion influences required rates of return.