QuestionConsider again the random sample as in item (3) above. Can you think of a suitable extension of the method-of-moment method to find an estimator of θ? (1) Suppose that X1,..., X, is a random sample from the Normal distributionN(0, a?) with parameter a > 0. Find the method-of-moment estimator of o.(2) Suppose that X1,...,X, is a random sample from the Gamma distribution withdensitya-leI(a)"and parameters a, 8 > 0. Using the fact, without proof, that the expected valueand variance of the Gamma distribution are given by a/3 and a/B?, respectively,S(r; a, 8) :I>0find the method-of-moment estimator of a and 3.(3) Suppose that X;...,X, is a random sample from a distribution with densityf(x; 8) = 0x-2, r e (8, 00)and parameter 6 > 0. What can you say about the method-of-moment estimatorof 0 as we defined it in the lectures?

According to Bartleby guildlines we have to solve first question and rest can be reposted…

(1) Suppose that X1,..., X, is a random sample from the Normal distribution N(0, a?) with parameter a > 0. Find the method-of-moment estimator of o. (2) Suppose that X1,...,X, is a random sample from the Gamma distribution with density -le r(a)" and parameters a, 8 > 0. Using the fact, without proof, that the expected value and variance of the Gamma distribution are given by a/ß and a/B2, respectively, S(r; a, 8) 1> 0 find the method-of-moment estimator of a and 3. (3) Suppose that X;...,X, is a random sample from a distribution with density f(x; 8) = 0x-2, r e (8, 00) and parameter 6 > 0. What can you say about the method-of-moment estimator of 0 as we defined it in the lectures?

(1) Suppose that X1,..., X, is a random sample from the Normal distribution N(0, a?) with parameter a > 0. Find the method-of-moment estimator of o. (2) Suppose that X1,...,X, is a random sample from the Gamma distribution with density -le r(a)" and parameters a, 8 > 0. Using the fact, without proof, that the expected value and variance of the Gamma distribution are given by a/ß and a/B2, respectively, S(r; a, 8) 1> 0 find the method-of-moment estimator of a and 3. (3) Suppose that X;...,X, is a random sample from a distribution with density f(x; 8) = 0x-2, r e (8, 00) and parameter 6 > 0. What can you say about the method-of-moment estimator of 0 as we defined it in the lectures?

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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