Answer the following:

We want to implement a Gibbs sampler to generate bivariate random vectors from the target distribution given by 7r(w, y) 0: exp(..":2 + 2mg 4y2), for x, y E (00, 00). (:1) Determine the conditional distributions of [X |Y = y] and [YIX = 1']. Describe a Gibbs sampler to generate samples from (27, y). (b) Set the initial value (X ("Kl/(0)) = (5,5). Run the Gibbs sampler for 6000 iterations and make a scatterplot of the sample path of the rst 50 iterations. (c) Use the samples generated in the last 5000 iterations to estimate the following expectations: EAXY) and E1,(\\/X2+Y2)