use r studio to finish the question, thanks

The governor of a prison wishes to assess the recidivism rate of prisoners released from his prison over a three year period. It turns out that ni 30 prisons were released in 2010 and within a three year period 16 of these had re- offended. While n = - 41 prisoners were released in 2015 and among these, 14 had re-offended within a three year period. You may assume that the probability that a prisoner released in 2010 re-offends within three years is independent of the probability that a prisoner released i 2015 re-offends within three years. You may also specify independent binomial models for the number of prisoners who re-offended who were released in 2010 and 2015. Further, you may place a Beta(2, 2) prior on 01 and 62 , the proportion who re-offend after being released in 2010 and 2015, respectively. 1. Consider first the data corresponding to prisoners who were released in 2010. Present a Monte Carlo approximation of an 80% credible interval using a Monte Carlo sample of size 200. Comment briefly on this credible interval. Compare this to the exact 80% credible interval. (10 marks) The governor of a prison wishes to assess the recidivism rate of prisoners released from his prison over a three year period. It turns out that ni 30 prisons were released in 2010 and within a three year period 16 of these had re- offended. While n = - 41 prisoners were released in 2015 and among these, 14 had re-offended within a three year period. You may assume that the probability that a prisoner released in 2010 re-offends within three years is independent of the probability that a prisoner released i 2015 re-offends within three years. You may also specify independent binomial models for the number of prisoners who re-offended who were released in 2010 and 2015. Further, you may place a Beta(2, 2) prior on 01 and 62 , the proportion who re-offend after being released in 2010 and 2015, respectively. 1. Consider first the data corresponding to prisoners who were released in 2010. Present a Monte Carlo approximation of an 80% credible interval using a Monte Carlo sample of size 200. Comment briefly on this credible interval. Compare this to the exact 80% credible interval. (10 marks)