Let X1, . . . , Xn+m be a random sample from the exponential distribution with parameter . Suppose that has the gamma prior

Let X1, . . . , Xn+m be a random sample from the exponential distribution with parameter θ. Suppose that θ has the gamma prior distribution with known parameters α and β. Assume that we get to observe X1, . . . , Xn, but Xn+1, . . . , Xn+m are censored.
a. First, suppose that the censoring works as follows: For i = 1, . . . , m, if Xn+I ≤ c, then we learn only that Xn+i ≤ c, but not the precise value of Xn+i. Set up a Gibbs sampling algorithm that will allow us to simulate the posterior distribution of θ in spite of the censoring.
b. Next, suppose that the censoring works as follows: For i = 1, . . . , m, if Xn+i ≥ c, then we learn only that Xn+i ≥ c, but not the precise value of Xn+i. Set up a Gibbs sampling algorithm that will allow us to simulate the posterior distribution of θ in spite of the censoring.