Question: 2 Jeremy Mixture Show that for likelihood f(x | #) and mixture prior TT ( 0) = EnI (0) + (1 - E) T2 (0),

2 Jeremy Mixture Show that for likelihood f(x | #) and

2 Jeremy Mixture Show that for likelihood f(x | #) and mixture prior TT ( 0) = EnI (0) + (1 - E) T2 (0), 0EO, the posterior is a mixture of T(0 | x) = Em(0 | x) + (1 -6) 72(0 (x), where Course Material for ISyE6420 by Brani Vidakovic is licensed under a Creative Commons Attribution- NonCommercial 4.0 International License. m.(x) = / f(x | 0):(0)do, i =1,2, and Emi (a") ( =Emi(x) + (1 -e)mz(x) Now we assume X | 0 ~ N(0, 80) and the prior for 6 is a mixture A ~ T(0) = =N(110, 60) + => (100, 200). Find the posterior and Bayes estimator for 0 if X = 98

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