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3. Suppose that Y1, Y2, Ym and X₁, X2, ..., Xm are independent normally distributed random samples from populations with means ₁ and 2 and variances 1² and 02², respectively. Is X - Y a consistent estimator of 2-₁? Justify your answer.

3. Suppose that Y1, Y2, Ym and X₁, X2, ..., Xm are independent normally distributed random samples from populations with means ₁ and 2 and variances 1² and 02², respectively. Is X - Y a consistent estimator of 2-₁? Justify your answer.

MATLAB: An Introduction with Applications
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 A Aa- Jabx X, X¹² A-ay-A- DS -12 Font 2. re to search 3. 5 ME Paragraph Styles Let Y₁, Y2, Y3, Y4, Ys and X1, X2, X9 be independent and normally distributed random samples from populations with means ₁ = 2 and 2 = 8 and variances 01²=5 and 02²= k, respectively. Suppose that P(X-Y> 10) = 0.02275, find the value of ₂² = k 6. DIK ENGLISH (SOUTH AFRICA) Suppose that Y1, Y2, Ym and X1, X2, ..., Xm are independent normally distributed random samples from populations with means ₁ and ₂ and variances 01² and 022, respectively. Is X-Y a consistent estimator of 2-₁? Justify your answer. 4. Suppose that Y₁, Y2,... Ym is a random sample of size m from Gamma(a = 3, B = 0), where is not known Check whether or not the maximum likelihood estimator is a minimum variance unbiased estimator of the parameter o AaBbCcDc AaBbCcDc AaBbC AaBbCct AaB AaBbcct AaBbCcD T Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle Subtle Em.. 0550 Suppose that a random sample X1, X2, X20 follows an exponential distribution with parameter p Check whether or not a pivotal quantity exixts, if it exists, find a 100(1 - α)% 91 confidence interval for p. Suppose that a random sample x is given by a probability density function (B-2), 0<x< B 0, otherwise 2 f(x) = {B² Without using MGF technique, prove or disapprove that i a is a pivotal quantity ( 23°C 19 BE
Transcribed Image Text:A A Aa- Jabx X, X¹² A-ay-A- DS -12 Font 2. re to search 3. 5 ME Paragraph Styles Let Y₁, Y2, Y3, Y4, Ys and X1, X2, X9 be independent and normally distributed random samples from populations with means ₁ = 2 and 2 = 8 and variances 01²=5 and 02²= k, respectively. Suppose that P(X-Y> 10) = 0.02275, find the value of ₂² = k 6. DIK ENGLISH (SOUTH AFRICA) Suppose that Y1, Y2, Ym and X1, X2, ..., Xm are independent normally distributed random samples from populations with means ₁ and ₂ and variances 01² and 022, respectively. Is X-Y a consistent estimator of 2-₁? Justify your answer. 4. Suppose that Y₁, Y2,... Ym is a random sample of size m from Gamma(a = 3, B = 0), where is not known Check whether or not the maximum likelihood estimator is a minimum variance unbiased estimator of the parameter o AaBbCcDc AaBbCcDc AaBbC AaBbCct AaB AaBbcct AaBbCcD T Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle Subtle Em.. 0550 Suppose that a random sample X1, X2, X20 follows an exponential distribution with parameter p Check whether or not a pivotal quantity exixts, if it exists, find a 100(1 - α)% 91 confidence interval for p. Suppose that a random sample x is given by a probability density function (B-2), 0<x< B 0, otherwise 2 f(x) = {B² Without using MGF technique, prove or disapprove that i a is a pivotal quantity ( 23°C 19 BE
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