Let X1, ...,Xn be a random sample from the EXP() distribution, and let the prior distribution of be EXP(). (i) Find the Bayes estimator

Let X1, ...,Xn be a random sample from the EXP(θ) distribution, and let the prior distribution of θ be EXP(β). (i) Find the Bayes estimator of θ and of μ = 1/θ

using the squared error loss. (ii) Obtain the 90% credible interval for θ and for μ if n = 6, x = 4, and β = 2.