Suppose we have the prior ㅠ (1) ~ Gamma (a, b) (where a, b > 0, and conditional on A, we have observations X1, X2, ..., Xn ∼ Xd Exp (A). Compute the posterior distribution π (λ)X1, X2,..., Xn).
Yet again, the posterior distribution for A is an Gamma distribution. What are its parameters? Enter your answer in terms of a b, n, and Σⁿᵢ₌₁ xi
(Enter Sigma_i(X_i) for Σⁿᵢ₌₁. Do not worry if the parser does not render properly; the grader works independently. If you wish to have proper rendering, enclose Sigma_i(X_i) by brackets.)
θ=___
k=___
Now, we examine two properties of the prior. Select the correct answer choice.
a. The prior is proper and is a conjugate prior.
b. The prior is improper and is a conjugate prior.
c. The prior is proper and is not a conjugate prior.
d. The prior is improper and is not a conjugate prior.