Let X1,..., X, be a random sample (i.i.d.) following Gamma(2, 3) for some unknown pa- rameter 3 > 0. (a) What is the MLE of 3? Derive it. Is the MLE of ß a consistent estimator for B? Prove/disprove it. (b) Hint: You may need continuous mapping theorem for convergence in probability. (c) ) What is the Method of Moments estimator of 3? Gamma(a, b) (d) for some a, b > 0. Derive the posterior distribution of 3 given (X1,... , X„) = (x1, ..., xn). Hint: For Gamma likelihood with known a (= 2) and unknown 3 (as is our case), the Now let's think like a Bayesian. Consider a prior distribution of 3 ~ %3| conjugate prior on 3 is a Gamma distribution. (e) of 3 assuming squared error loss? Using the same prior as in the previous sub-question, what is the Bayes estimator
Let X1,..., X, be a random sample (i.i.d.) following Gamma(2, 3) for some unknown pa- rameter 3 > 0. (a) What is the MLE of 3? Derive it. Is the MLE of ß a consistent estimator for B? Prove/disprove it. (b) Hint: You may need continuous mapping theorem for convergence in probability. (c) ) What is the Method of Moments estimator of 3? Gamma(a, b) (d) for some a, b > 0. Derive the posterior distribution of 3 given (X1,... , X„) = (x1, ..., xn). Hint: For Gamma likelihood with known a (= 2) and unknown 3 (as is our case), the Now let's think like a Bayesian. Consider a prior distribution of 3 ~ %3| conjugate prior on 3 is a Gamma distribution. (e) of 3 assuming squared error loss? Using the same prior as in the previous sub-question, what is the Bayes estimator
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question

Transcribed Image Text:Let X1,..., Xn be a random sample (i.i.d.) following Gamma(2, 3) for some unknown pa-
rameter 3 > 0.
(а)
What is the MLE of 3? Derive it.
Is the MLE of Ba consistent estimator for 3? Prove/disprove it.
(b)
Hint: You may need continuous mapping theorem for convergence in probability.
(c) (
What is the Method of Moments estimator of 3?
(d)
Gamma(a, b)
Now let's think like a Bayesian. Consider a prior distribution of 3
for some a, b > 0. Derive the posterior distribution of 3 given (X1, .
Hint: For Gamma likelihood with known a (= 2) and unknown 3 (as is our case), the
X„) = (x1,. .. , xn).
....
conjugate prior on 3 is a Gamma distribution.
(e)
of 3 assuming squared error loss?
Using the same prior as in the previous sub-question, what is the Bayes estimator
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