Please see attached mathematical statistics question below. How to show the unbiased estimator of theta has variance2theta^2/n. Please do not reject question if you do not know how to solve this problem. Allow another expert a chance to answer this question. **Unbiased Estimator Problem**Let $ X_1, \ldots, X_n $ denote a random sample from a normal distribution with mean zero and variance $ \theta > 0 $. Show that $ \frac{1}{n} \sum_{i=1}^{n} X_i^2 $ is an unbiased estimator of $ \theta $ and has variance $ 2\theta^2 / n $.

It is a fact of statistics . It is widely used in probability .X1,X2,......,Xn ~ iid N(0,θ)Then , E(Xi)=0 and V(Xi)=θ , i=1(1)nE(1n∑i=1nXi2)= E(X12) = V(X1)+E2(X1) = θ Hence , 1n∑i=1nXi2 is an unbiased estimator of θ V( 1n∑i=1nXi2 ) =V( X12)n = E(X14) - E2(X12) Now , to find E(X14) , we proceed :Lemma : If Y be a normal variable with mean μ and variance σ2, then E(Y4) =3σ4Here , X1θ ~ N(0,1)E[(X1θ)4] =3 , E(X14) =3θ2V( 1n∑i=1nXi2 ) =V( X12)n = E(X14) - E2(X12) n =3θ2-θ2n =2θ2n

Answered: Let X1,..., Xn denote a random sample…

Math

Probability

Let X1,..., Xn denote a random sample from a normal distribution with mean zero and variance 0 > 0. Show that ", X? is an unbiased estimator of 0 and has variance 26 /n.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: It is easy to create a simple mathematical model using technology. Consider the scenario below.…

A: We have given projected profit for the given 3 types of businesses over 6 months Month…

Q: A study found a positive correlation between IQ and making good economic choices. One possible…

A: Lurking variable can identify a strong relationship between variables or it can hide the true…

Q: When working with a Chi-Squared test, we need data to be Normally distributed True False

Q: In Excel, for each of the 2 majors calculate the mean, median, minimum, maximum, range, and standard…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: Explain how standard deviation is calculated and how does it play an important role to determining…

Q: True or False: For both AIC and BIC (two statistics we often use to compare model fit), the model…

A: Solution: AIC ( Akaike's Information Criteria ) and BIC ( Bayesian Information Criteria ) are the…

Q: A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose…

A: Average peak wave height μ=16.4You just want to test the hypothesis that the average wave height is…

Q: Part 1 of 5 (a) State the appropriate null and alternate hypotheses. H1: This hypothesis test is a…

A: mu = 2.1 xabr = 1.95 n = 54 sigma = 0.4

Q: there is no work shown how to get standard deviation or Variance if I could have my questions back…

A: Answer:- Given, 28% of U.S. employees who are late for work blame oversleeping. That is,…

Q: c. The test statistic | z 2.182 (please show your answer to 3 decimal places.)

A: From the provided information, The level of significance (α) = 0.01 The test is one tailed.

Q: How to find the variance, explain the formula

A: Mean:Mean is a measure of center in case of quantitative data. Mean of a data set is the sum of the…

Q: 3b. If the writing scores have a population standard deviation of o = 10, what conclusion should we…

A: Given A random sample of size ( n ) = 25 is taken The average grade ( M ) = 76 µ = 70

Q: State three examples where similar averages are associated with very different distributions Go…

A: Given : State three examples where similar averages are associated with very different…

Q: Please Find the mean and variance of Binomial variable X having p=0.09 and n=2.

Q: A type I error will occur if the actual mean of the length of time to play a game is equal to…

Q: Please submit the answer via a PDF document or Word document. **Independent t-test** Use the…

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any…

Q: Before using these mean squares what does we must calculate?

A: Mean squares is nothing but the sum of the squares of the mean of the group divided by the degrees…

Q: This my third time posting the same question. Because no one answer it straight to me. I already…

A: 1)From the provided information, The sample number of students watching video (n) = 19 The number of…

Q: Briefly explain specifically why categorical and quantitative variables require different methods in…

A: Categorical and quantitative variables require different methods to describe their distributions…

Q: Provide an example scenario for which you would use ANOVA and explain what the calculated F value…

A: Suppose a sample of diabetes patients and non diabetes patients weight is taken . A One Way ANOVA…

Q: how do you find the variance of the mean squared errors from this tabe

A: We need to find the variance of MSE of the given data:Year1969197319751979198319881991# Attending…

Q: writing a null hypothesis for the bivariate relationship shown in the SPSS ou

A: Given:

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

100%

Please see attached mathematical statistics question below.

How to show the unbiased estimator of theta has variance
2theta^2/n.

Please do not reject question if you do not know how to solve this problem. Allow another expert a chance to answer this question.

**Unbiased Estimator Problem**

Let $ X_1, \ldots, X_n $ denote a random sample from a normal distribution with mean zero and variance $ \theta > 0 $. Show that $ \frac{1}{n} \sum_{i=1}^{n} X_i^2 $ is an unbiased estimator of $ \theta $ and has variance $ 2\theta^2 / n $.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

If no data values are given but the mean and standard deviation is given how do I find the variance with just this information?
Please answer the solution from the problem. Im very needed in 30 minutes thank u and no reject please. Thank u
what do the mean deviation, variance and standard deviation all have in common? How is this helpful with the calculations of these variabvariables.
the standard deviation however is not squared? don't we have to square those first because SD is variance squared?
Help me please
Please solve part c, d and e only. DO NOT SOLVE PART a AND b. I need answers for part c, part d and part e.
jake suspects that individuals with an optimistic world view live longer than individuals with a pessimistic view. Sate the research hypothesis the null hypothesis cases independent variable dependent variable
STATISTICS.docx - Google Docs + A docs.google.com/document/d/1Xgqq34HC4kub_OY7HprnxliVKF2wTIZI/edit 2. One wishes to estimate the average age of a student population. It is known that the standard deviation is 2 years. A sample of 50 students is taken and the mean of these students is 23.2 years. What is the point estimate of the population mean? b. Find a 95% confidence interval for the pop. mean. а. 3:26 AM P Type here to search W 36°F Mostly clear * 4) 12/15/2021