Sorry yes,
The estimator is Theta hat3 = theta (an unbiased estimator)
Theta hat3 = c*(theta hat 1) + (1-c)*theta hat2
And if it helps at all, MSE(theta hat3) is smallest at c=1/3. This is all from previous steps. Thank you!
Homework Answers
Add Answer to:
Sorry yes,
The estimator is Theta hat3 = theta (an unbiased estimator)
Theta hat3 = c*(theta...
A) Find the variance of each unbiased estimator. b) Use the Central Limit Theorem to create an ap...
a) Find the variance of each unbiased estimator.
b) Use the Central Limit Theorem to create an approximate 95%
confidence interval for theta.
c) Use the pivotal quantity Beta(alpha=13, beta=13) to create an
approximate 95% confidence interval for theta.
d) Use the pivotal quantity Beta(alpha=25, beta=1) to create an
approximate 95% confidence interval for theta.
Suppose that Xi, , x25 are i.i.d. Unifom(0,0), where θ is unknown. Consider three unbiased estimators of 6 25 26 25 25 26 max (X...,...
(a) Are they unbiased estimators for µ? (b) Compute the MSE for all the 4 estimators. (c) Which one is the best estimat...
(a) Are they unbiased estimators for µ?
(b) Compute the MSE for all the 4 estimators.
(c) Which one is the best estimator for µ? Why.
PLEASE answer all parts, thanks
Let X1, X2, ..., X, be and i.i.d. sample from some distribution with mean y and variance o? Let us construct several estimators for . Let îi = X, iz = X1, A3 = (X1 + X2)/2, W = X1 + X2 (a) Are they unbiased estimators for ?...
Please give detailed steps. Thank you. 5. Let {X1, X2,..., Xn) denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the inte...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the interval I-1, 1]. Recall that this means the density function fu satisfies for(z-a: a.crwise. 1 u(z), -1ss1, a) Find thc cxpccted valuc and the variancc of U. We now consider estimators for the expected value of U which use a sample of size 2 Let Xi and X2 be independent random variables with the same distribution as U. Let X = (X1 +...
I figured out 1,2 and 3 but I’m stuck on 4 and 5. Please help me...
I
figured out 1,2 and 3 but I’m stuck on 4 and 5. Please help me out
if you can!! I know the quality isn’t the greatest, I’m sorry!!
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will prepare you for the exam. Please...
Please give detailed steps. Thank you. 5. Let {X, : i-1..n^ denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning. I have no...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning.
I have no clue how to do these. I know the image quality is iffy
but please help as best you can
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will...
R Programming In this section, we will expand upon some of the ideas we have incorporated...
R Programming
In this section, we will expand upon some of the ideas we have incorporated in the homework. For this entire problem, we will use the Normal distribution. For all the simulated datasets, we wil assume a mean of μ-10 and a standard deviation of σ-3. Consider the following estimators for u: 1. X 2. Q2, the sample median 3. (Q1 Qs), the average of the first and third sample quartiles 4. XI, the first observation As you have...
Which of the following statements is true? (a) If the calculated value of F statistic is...
Which of the following statements is true? (a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. (b) The F statistic is always nonnegative as SSR, is never smaller than SSRur. (C) Degrees of freedom of a restricted model is always less than the de- grees of freedom of an unre- stricted model. (d) The F statistic is more flexible than the t statistic to...
Please answer Problems 1-5 (with all the parts) and please show the work/steps! Thank you! 1/2...
Please answer Problems 1-5 (with all the parts) and please show
the work/steps! Thank you!
1/2 STA103_HW6.pdf Due Friday Dec 7th Problem 1. (problem 10.3 page 194) We have a simple random sample of size 4 from a population with mean u. Consider the following two estimators of u 10 10 a. Show that both μ1 and μ2 are unbiased estimators for μ. b. Which one is better? Fully justify your answer Problem 2. (Problem 10.4 page 194) Suppose that...
a) Find the variance of each unbiased estimator.
b) Use the Central Limit Theorem to create an approximate 95%
confidence interval for theta.
c) Use the pivotal quantity Beta(alpha=13, beta=13) to create an
approximate 95% confidence interval for theta.
d) Use the pivotal quantity Beta(alpha=25, beta=1) to create an
approximate 95% confidence interval for theta.
Suppose that Xi, , x25 are i.i.d. Unifom(0,0), where θ is unknown. Consider three unbiased estimators of 6 25 26 25 25 26 max (X...,...
(a) Are they unbiased estimators for µ?
(b) Compute the MSE for all the 4 estimators.
(c) Which one is the best estimator for µ? Why.
PLEASE answer all parts, thanks
Let X1, X2, ..., X, be and i.i.d. sample from some distribution with mean y and variance o? Let us construct several estimators for . Let îi = X, iz = X1, A3 = (X1 + X2)/2, W = X1 + X2 (a) Are they unbiased estimators for ?...
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
3. (5 marks) Let U be a random variable which has the continuous uniform distribution on the interval I-1, 1]. Recall that this means the density function fu satisfies for(z-a: a.crwise. 1 u(z), -1ss1, a) Find thc cxpccted valuc and the variancc of U. We now consider estimators for the expected value of U which use a sample of size 2 Let Xi and X2 be independent random variables with the same distribution as U. Let X = (X1 +...
I
figured out 1,2 and 3 but I’m stuck on 4 and 5. Please help me out
if you can!! I know the quality isn’t the greatest, I’m sorry!!
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will prepare you for the exam. Please...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
I REALLY need numbers 2 and 3 and 5 by like tomorrow morning.
I have no clue how to do these. I know the image quality is iffy
but please help as best you can
Homework1 STA4322 Homework 1, Spring 2019 Please turn in your own work, though you may discuss the problems with classmates, the TA, the Professor, the internet, etc. The most important thing is that you understand the problems and how they are solved as they will...
R Programming
In this section, we will expand upon some of the ideas we have incorporated in the homework. For this entire problem, we will use the Normal distribution. For all the simulated datasets, we wil assume a mean of μ-10 and a standard deviation of σ-3. Consider the following estimators for u: 1. X 2. Q2, the sample median 3. (Q1 Qs), the average of the first and third sample quartiles 4. XI, the first observation As you have...
Which of the following statements is true? (a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. (b) The F statistic is always nonnegative as SSR, is never smaller than SSRur. (C) Degrees of freedom of a restricted model is always less than the de- grees of freedom of an unre- stricted model. (d) The F statistic is more flexible than the t statistic to...
Please answer Problems 1-5 (with all the parts) and please show
the work/steps! Thank you!
1/2 STA103_HW6.pdf Due Friday Dec 7th Problem 1. (problem 10.3 page 194) We have a simple random sample of size 4 from a population with mean u. Consider the following two estimators of u 10 10 a. Show that both μ1 and μ2 are unbiased estimators for μ. b. Which one is better? Fully justify your answer Problem 2. (Problem 10.4 page 194) Suppose that...
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