Exercise6.3 Let Y1, ...,Yn f (y), where f (y) belongs tothe(one-parameter)exponentialfamily, i.e. thesupportsupp( f ) does

Exercise6.3 Let Y1, ...,Yn ∼ fθ (y), where fθ (y) belongs tothe(one-parameter)exponentialfamily, i.e. thesupportsupp( fθ ) does notdependon θ and fθ (y) = exp{c(θ)T(y)+d(θ)+S(y)}, y ∈

supp( fθ ).

1. Showthattheconjugatepriorfamilyfor θ is πα,β (θ) ∝ exp{αc(θ)+βd(θ)}.

2. Find aconjugatepriorfortheparameter λ of thePoissondistribution Pois(λ).