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v) Find a sufficient statistic for 0. (v) Suppose the prior distribution of e is given by -ga-le-A0, 0> 0; fe(0) = { r(a) 0, otherwise. Find the posterior distribution of O. (vi) Based on a = 2, = 4 and the data x = 0.45, x2 = 0.38 and xz = 0.62, calculate the (1) posterior mean and (2) posterior mode of the distribution obtained in part (v) and (3) maximum likelihood estimate of 0.

v) Find a sufficient statistic for 0. (v) Suppose the prior distribution of e is given by -ga-le-A0, 0> 0; fe(0) = { r(a) 0, otherwise. Find the posterior distribution of O. (vi) Based on a = 2, = 4 and the data x = 0.45, x2 = 0.38 and xz = 0.62, calculate the (1) posterior mean and (2) posterior mode of the distribution obtained in part (v) and (3) maximum likelihood estimate of 0.

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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part 4 5 6

Question 5 Let X1, X2, ..., X, be a random sample from a distribution with probability density func- tion Ox0-1, 0<I < 1; 0, f(x|0) = otherwise, where 0 > 0. (i) Find the maximum likelihood estimate of 0. (ii) Find the maximum likelihood estimate of P(X < 1/2). (iii) Find the Cramer-Rao lower-bound for the variances of unbiased estimators of 0. (iv) Find a sufficient statistic for 0. (v) Suppose the prior distribution of e is given by -ga-le-N0, 0> 0; fe(0) = { r(a) 0, otherwise. Find the posterior distribution of O. (vi) Based on a = 2, A = 4 and the data x1 = 0.45, x2 = 0.38 and r3 = 0.62, calculate the (1) posterior mean and (2) posterior mode of the distribution obtained in part (v) and (3) maximum likelihood estimate of 6.
Transcribed Image Text:Question 5 Let X1, X2, ..., X, be a random sample from a distribution with probability density func- tion Ox0-1, 0<I < 1; 0, f(x|0) = otherwise, where 0 > 0. (i) Find the maximum likelihood estimate of 0. (ii) Find the maximum likelihood estimate of P(X < 1/2). (iii) Find the Cramer-Rao lower-bound for the variances of unbiased estimators of 0. (iv) Find a sufficient statistic for 0. (v) Suppose the prior distribution of e is given by -ga-le-N0, 0> 0; fe(0) = { r(a) 0, otherwise. Find the posterior distribution of O. (vi) Based on a = 2, A = 4 and the data x1 = 0.45, x2 = 0.38 and r3 = 0.62, calculate the (1) posterior mean and (2) posterior mode of the distribution obtained in part (v) and (3) maximum likelihood estimate of 6.
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