Let X₁, X12, Xim and X21, X22X2n be two independent random samples ofsize n, and n₂ from two normal populations N(₁, 0) and N(2, 2) respectively.(a) Derive the maximum likelihood estimators (mle's) of all the parameters in the firstpopulation (X₁). Using analogy, state the mle's of the parameters of the secondpopulation.(b) Find the pooled estimator of the common variance when it is assumed that of =o=0². Suggest an unbiased estimator of o².(c) Assuming both n₁ and n₂ are small, suggest a pivotal function that can be used toderive a (1-a) x 100% confidence interval for (#4₁-4₂) when o² = 0 = 0².

Step: 1Let be two independent random samples of size n1 and n2 from two normal populations…

Answered: e maximum likelihood estimators (mle's)…

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...

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An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @
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X. is found to be 19.1, and the A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, sample standard deviation, s, is found to be 4.9. (a) Construct a 96% confidence interval about u if the sample size, n, is 39. (b) Construct a 96% confidence interval about u if the sample size, n, is 68. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about u if the sample size, n, is 39. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 14, what conditions must be satisfied to compute the confidence interval? (a) Construct a 96% confidence interval about u if the sample size, n, is 39. Lower bound: Upper bound: (Round to two decimal places as needed.) (b) Construct a 96% confidence interval about u if the sample size, n, is 68. Lower bound: ; Upper bound: (Round to two decimal places as needed.) How does increasing the sample…

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