Exercise7.3 Let Y1, ...,Yn exp(). 1. In Example6.8,wefoundthatthenoninformativeJeffreyspriorfor is () 1/. Whatis the Bayesestimatorfor

Exercise7.3 Let Y1, ...,Yn ∼ exp(θ).

1. In Example6.8,wefoundthatthenoninformativeJeffreyspriorfor θ is π(θ) ∝ 1/θ. Whatis the Bayesestimatorfor μ = EY = 1/θ w.r.t.thispriorandtheweightedquadraticloss L(μ,a) = (a−μ)2 μ2 ?
2. Calculate theriskoftheBayesestimatorfromthepreviousparagraphandcompareitwiththat of theMLEof μ. IstheMLEadmissible?