Question

For all of following, calculate the A) Posterior Distribution B)Bayes estimator of θ C) Predictive probability

1) yi iid∼ Bern(θ), i = 1, . . . , n1, and yj iid∼ Bern(2θ), j = n1 + 1, . . . , n1 + n2, yi and yj mutually independent .   Use θ ∼ Beta(α, β) for prior

2) Same as problem 1 but with Bin(Mi,θ) and Bin(Mi, 2θ) instead of Bern(θ) and Bern(2θ), respectively. Use θ ∼ Beta(α, β) for prior

3) Same as problem 1 but with Poisson(λ) and Poisson(2λ) instead of Bern(θ) and Bern(2θ), respectively. Use λ ∼ Gamma(α, β) for prior

Answer 1

C4) I-1 ไม่ Parf