We have i.i.d. observations X₁,..., Xn each with pdf 20xe -0x² x > 0, 9 f(x|0) 0, otherwise. Here> 0 is an unknown param

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We Have I I D Observations X Xn Each With Pdf 20xe 0x X 0 9 F X 0 0 Otherwise Here 0 Is An Unknown Param 1 (82.63 KiB) Viewed 54 times

We have i.i.d. observations X₁,..., Xn each with pdf 20xe -0x² x > 0, 9 f(x|0) 0, otherwise. Here> 0 is an unknown parameter. We are going to do a Bayesian analysis. As prior on the parameter we use a Gamma(a, X)-distribution, with some fixed choices for a, λ > 0. (a) Determine the posterior density up to a normalizing constant. (b) Which common distribution is the posterior? (c) Determine the posterior mean B. (Use the table of expectations in the Ap- pendix of the book.) =