Exercise6.6 Continue Exercise2.3.AssumeaGammaprior Gamma(,) for . 1. Is itaconjugatepriorforthedata? 2. Find theBayesestimatorsw.r.t.thesquarederrorof (a) (b) expectedlifetimesofasingleelementandanentiredevicecontaining k

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Exercise6.6 Continue Exercise2.3.AssumeaGammaprior Gamma(α,β) for θ.

1. Is itaconjugatepriorforthedata?

2. Find theBayesestimatorsw.r.t.thesquarederrorof

(a) θ

(b) expectedlifetimesofasingleelementandanentiredevicecontaining k elements

(c) probability thatadevicewilloperateforatleast a hours 3. Are theaboveBayesestimatorsconsistentfromafrequentistpointofview?

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