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(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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Consider 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 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 a-le I(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/3 and a/B?, respectively, S(r; a, 8) : I>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?
Transcribed Image Text:(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 a-le I(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/3 and a/B?, respectively, S(r; a, 8) : I>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?
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