Exercise6.5 Let Y1, ...,Yn Geom(p). 1. ShowthatafamilyofBetapriors Beta(,) for p is aconjugatefamilyofpriorsforgeometric data, derivethecorrespondingposteriordistributionandfindtheBayesestimatorof p w.r.t.the

Exercise6.5 Let Y1, ...,Yn ∼ Geom(p).

1. ShowthatafamilyofBetapriors Beta(α,β) for p is aconjugatefamilyofpriorsforgeometric data, derivethecorrespondingposteriordistributionandfindtheBayesestimatorof p w.r.t.the squared error.

2. Find Jeffreysnoninformativepriorfor p and repeatthepreviousquestionforit.