Let X1,..., X, be a random sample from a Poisson distribution with mean A.(i) Find the Cramér-Rao lower bound for the variances of unbiased estimators of A.(ii) Find a uniformly minimum variance unbiased estimator of A.(iii) Is the maximum likelihood estimator of A asymptotically unbiased?(iv) Find the Cramér-Rao lower bound for the variances of unbiased estimators ofT(A) = e-A.(v) It can be shown that 7 = [(n – 1)/n]E Xi is an unbiased estimator of T in (iv).Find the variance Var(7) and compare it with the Cramér-Rao lower bound (of(iv)).

According to Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

Answered: Let X1,..., X, be a random sample from…

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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tion 21. An investor is considering two types of investment. She is quite satisfied that the expected return on investment 1 is higher than the expected return on investment 2. However, she is quite concerned that the risk associated with investment 1 is higher than that of investment 2. To help make her decision, she randomly selects seven monthly returns on investment 1 and ten monthly returns on investment 2. She finds that the sample variances of investments 1 and 2 are 225 and 118, respectively. a) Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2? b) Estimate with 95% confidence the ratio of the two population variances. c) Briefly describe what the interval estimate tells you.
, A manufacturer of sunflower oil uses machines to distribute liquid ingredients into bottles that move along a filling line. The machine that distributes is working properly when 8 ounces are distributed. Suppose that the average amount distributed in a particular sample of 35 bottles is 7.91 ounces. Assume that the variance of the process is known to be 0.03 ounces squared. Is there evidence that the machine should be stopped (when not 8 ounces are distributed), and production wait for repairs? The lost production from a shutdown is potentially so great that management feels that the level of confidence in the analysis should be 99%.
A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs, model A and model B. Independent random samples of the two models were taken. Analysis of 15 bulbs of model A showed a mean lifetime of 1348 hours and a standard deviation of 81 hours. Analysis of 11 bulbs of model B showed a mean lifetime of 1351 hours and a standard deviation of 109 hours. Assume that the populations of lifetimes for each model are normally distributed and that the variances of these populations are equal. Construct a 99% confidence interval for the difference H-, between the mean lifetime u, of model A bulbs and the mean lifetime u, of model B bulbs. Then find the lower limit and upper limit of the 99% confidence interval, Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.) Lower limit: Upper limit: Explanation Check 2021 McGraw-Hill Education. Al Rights Reserved…
A simple random sample without replacement was used to select 5 clusters from a population of 29 clusters. From each selected sample cluster simple random sampling without replacement was used to select samples of secondary units. For this data find an estimate of the population total and the population mean along with their estimated variances. clmemb clsize yval [1,] [2,] [3,] [4,] [5,] [6,] [7,] [8,] [9,] [10,] [11,] [12,] [13,] [14,] [15,] [16,] [17,] [18,] [19,] [20,] [21,] [22,] [23,] [24,] [25,] [26,] [27,] [28,] [29,] [30,] [31,] [32,] [33,] 1 20 46.07 20 45.54 20 43.07 1 1. 1 20 49.29 1 20 44.35 1 20 45.21 2 33 44.11 2 33 42.19 2 33 44.42 2 33 40.05 2 33 43.88 2 33 47.45 2 33 40.41 2 33 43.24 3 22 35.42 3 22 35.46 3 22 36.34 3 22 35.25 4 40 38.67 4 40 34.73 4 40 39.28 4 40 35.26 4 40 39.84 4 40 40.32 4 40 40.03 4 40 38.15 4 40 38.69 4 40 39.38 18 47.48 18 44.78 5 18 44.37 18 44.97 5 18 49.20
a) Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 2.6282.6681 is the standard deviation of the second sample. B) Find the F-test statistic to test the claim that the population variances are equal. Both distributions are normal. The standard deviation of the first sample is 4.15966.3763 is the standard deviation of the second sample.
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Assume that the helium porosity (in percentage) of coal samples taken from anyparticular seam is normally distributed with true population variance 0.36.(a) Compute a 95% two-sided CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85. (b) How large a sample size is necessary if the width of the 95% two-sided CI is to be 0.5? (c) Compute a 98% upper one-sided CI for true average porosity of another seam based on 16 specimens with a sample average porosity of 4.56.show major intermediate steps.
A manufacturing company is interested in buying one of two different kinds of machines for production purposes. The first machine was run for 20 hours. It produces on average of 40 items per hour with variance of 8 items2. The second machine was run for 15 hours. It produces on average 50 items per hour with variance of 10 items2. Assume that the production per hour for each machine is (approximately) normally distributed and there a homogeneity between the populations' variances of the number of items produced by the 2 machines Compute 90% confidence interval for the difference between the two means. What is the tabulated value What is the S.E value What Is the lower and upper bound
A light bulb manufacturer wants to compare the mean lifetimes of two of its light bulbs, model A and model B. Independent random samples of the two models were taken. Analysis of 10 bulbs of model A showed a mean lifetime of 1347 hours and a standard deviation of 92 hours. Analysis of 13 bulbs of model B showed a mean lifetime of 1380 hours and a standard deviation of 111 hours. Assume that the populations of lifetimes for each model are normally distributed and that the variances of these populations are equal. Construct a 95% confidence interval for the difference −μ1μ2 between the mean lifetime μ1 of model A bulbs and the mean lifetime μ2 of model B bulbs. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. Upper Limit Lower Limit:
The graphs show a violation of the assumption of (check all that apply) normality homogeneity of variance
Consider the model (1-B)(1-0.2B)X_t = (1-0.5B)W_t find the forecasts for one, two and three steps ahead and calculate the variance of the one, two, and three steps ahead forecast errors

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