Cauchy sampling model suppose one observes a random sample from a cauchy density with location θ and scale parameter 1. if a uniform prior is placed on θ, then the posterior density is given (up to a proportionality constant) by i=1 suppose one observes the data 0, 10, 9, 8, 11, 3, 3, 8, 8, 11. a) using the r command seq, set up a grid of values of θ from −2 to 12 in steps of 0.1. b) compute the posterior density on this grid. c) plot the density and comment on its main features. d) compute the posterior mean and posterior standard deviation of θ.