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(3) Let x1, X2, ·. , Xn Gamma(2, a), à > 0, a > 0. That is the density of x1 is cra-le-àx, if x > 0, Г(а) f(x) = 0, otherwise. Find the likelihood function of 0 = (2, a). If a = 3, can an MLE of à fail to exist with positive probability: If not, find the MLE. The following "answers" have been proposed. (a) The likelihood function of (2, a) is a-1 ana Xi (T(a))" when all x; > o and zero otherwise. When a = 3, the MLE of 2 is 3n Division by o would occur only with probability zero, therefore, the MLE exists. (b) The same as the answer in part (a) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (c) The likelihood function of (2, a) is a-1 ana e (T(a))" i=1 when all x; > o and zero otherwise. When a = 3, the MLE of 2 is 3n Division by o would occur only with probability zero, therefore, the MLE exists. (d) The same as the answer in part (c) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (e) None of the above The correct answer is (a) (b) (c) (d) (e) N/A (Select One)

(3) Let x1, X2, ·. , Xn Gamma(2, a), à > 0, a > 0. That is the density of x1 is cra-le-àx, if x > 0, Г(а) f(x) = 0, otherwise. Find the likelihood function of 0 = (2, a). If a = 3, can an MLE of à fail to exist with positive probability: If not, find the MLE. The following "answers" have been proposed. (a) The likelihood function of (2, a) is a-1 ana Xi (T(a))" when all x; > o and zero otherwise. When a = 3, the MLE of 2 is 3n Division by o would occur only with probability zero, therefore, the MLE exists. (b) The same as the answer in part (a) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (c) The likelihood function of (2, a) is a-1 ana e (T(a))" i=1 when all x; > o and zero otherwise. When a = 3, the MLE of 2 is 3n Division by o would occur only with probability zero, therefore, the MLE exists. (d) The same as the answer in part (c) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (e) None of the above The correct answer is (a) (b) (c) (d) (e) N/A (Select One)

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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MLE: Maximum likelihood estimation

(3) Let x1, X2, ·, Xn iid Gamma(2, a), 2 > 0, a > 0. That is the density of x1 is 24 za-le-ix, if x > 0, Г(а) 0, f(x) = otherwise. Find the likelihood function of e = (2, a). If a = 3, can an MLE of a fail to exist with positive probability: If not, find the MLE. The following ¨answers" have been proposed. (a) The likelihood function of (2, a) is a-1 n ana || Xi (T'(a))" i=1 when all x; > 0 and zero otherwise. When a = 3, the MLE of a is 3n = Division by o would occur only with probability zero, therefore, the MLE exists. (b) The same as the answer in part (a) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (c) The likelihood function of (2, a) is a-1 n 2na (T(@))" i=1 when all x; > 0 and zero otherwise. When a = 3, the MLE of a is 3n î = Division by o would occur only with probability zero, therefore, the MLE exists. (d) The same as the answer in part (c) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (e) None of the above The correct answer is (a) (b) (c) (d) (e) N/A (Select One)
Transcribed Image Text:(3) Let x1, X2, ·, Xn iid Gamma(2, a), 2 > 0, a > 0. That is the density of x1 is 24 za-le-ix, if x > 0, Г(а) 0, f(x) = otherwise. Find the likelihood function of e = (2, a). If a = 3, can an MLE of a fail to exist with positive probability: If not, find the MLE. The following ¨answers" have been proposed. (a) The likelihood function of (2, a) is a-1 n ana || Xi (T'(a))" i=1 when all x; > 0 and zero otherwise. When a = 3, the MLE of a is 3n = Division by o would occur only with probability zero, therefore, the MLE exists. (b) The same as the answer in part (a) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (c) The likelihood function of (2, a) is a-1 n 2na (T(@))" i=1 when all x; > 0 and zero otherwise. When a = 3, the MLE of a is 3n î = Division by o would occur only with probability zero, therefore, the MLE exists. (d) The same as the answer in part (c) except that in the expression of the MLE division by zero occurs with positive probability and hence the MLE does not exist. (e) None of the above The correct answer is (a) (b) (c) (d) (e) N/A (Select One)
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