4. In this question, we are going to test the bias and efficiency of estimators.For this question assume that X follows an unknown distribution; however,we do know that E[X] μ and Var[X] = 0²=Moreover, we are able to somehow sample n i.i.d. data from the populationX. Let's denote our sample as {X₁, X2,,Xn}Let's focus on the mean, ul.nSo far, our best estimate of our sample is the sample mean X = ½ Σï_₁ X₁.Nevertheless, you may wake up one day and think "why should we compute thesample mean every time? It feels so tedious."You have decided to rather use the following estimator:2X₁ + X2 + X3 + + Xnn+1Ô(a) Calculate the bias of this estimator to respect to the population mean.Show all steps in the calculation.(b) Is this estimator unbiased for μ?(c) Calculate variance of this estimator. Show your work.(d) Assume n > 1. Compare the efficiency of ô and X. Which one wouldyou choose as an estimator for the population mean?

Answered: Image /qna-images/answer/954a640d-712f-4fbe-9442-093d49b2bd60.jpg

Answered: 4. In this question, we are going to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A study is conducted to determine factors in solving missing persons cases. The outcome is Y; which is equal to 1 if the i-th missing person case is unsolved and 0 if it is solved. Let covariate X1; be an indicator equal to 1 if the i-th case is female and 0 for male. Let X2i be a categorical covariate of age group for the i-th case. Categories are less than 14 years old (base level/group), between 14 and 19 years old, and older than 19 years. Set u = P(Y = 1) and the following model is fit: logit(u) = Bo + BịI(Female) + B2I(14 to 19 yrs old) + B3I(> 19 yrs old) The output from the model is below: Estimate S.E. p-value Bo -4.565 0.128 0.380 0.087 B2 Вз -0.198 0.042 0.163 1.128 0.133 a. Using the logistic regression output, calculate the estimated odds ratio of a case being unsolved (again Y=1 is unsolved and Y=0 is solved) comparing females to males (female is the numerator odds) of the same age. Interpret this odds ratio in context of the problem. iii b. Create a 95% confidence…
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5. Suppose the number of days it takes you to get a flu shot after it is available follows this equation: Y₂ = 30 - 2X₁ where y, is the number of days until you get the flu shot, and X, is the number of people you know who have the flu. Further, suppose on average you know 2.3 people who have the flu, with standard deviation 5. Suppose that the population has size m = 10. (a) Find the average time until you get the flu shot after it is available. (b) Find the standard deviation of time until you get the flu shot after it is available. (c) What is EY;?
I need this question completed in 10 minutes with full handwritten working out
The researcher would like to determine if these data provide convincing evidence that the true mean amount of time volunteers who were given training held their breath is greater than volunteers without training. Let μ1 = the true mean amount of time that volunteers who were given training held their breath and μ2 = the true mean amount of time that volunteers without training held their breath. What are the appropriate hypotheses?
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Hello. I need solutions of question 4 and 5. Thanks in advance dor your help.
Suppose x has a distribution with a mean of 80 and a standard deviation of 45. Random samples of size n = 36 are drawn. Find P(x < 87.5) Please show the steps to finding the answer and use a ti-83+ calculator since this is what I am working with.

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