Question

I'm very confused about how to do it. I think you have to use R to solve the question. Any help would be appreciated thanks.

Suppose you work for a casino and have been tasked with determining whether a particular six-sided die is fair, in which case the probability is exactly 1/6 that a roll of the die results in any one of its six face values. Suppose there are two commonly used sets of face value weights among biased dice on the market, with probabilities given in Table 1. Also included in Table 1 are the fair-die probabilities, and we will assume that exactly one of these three possible models apply to the die being examined. After 100 automated rolls by a machine, the observed frequencies were as given in the second-to-last row of Table 1 Given these observed data, the likelihoods for the three models can be computed in R using the multinomial distribution freq <- c(14, 20, 14, 19, 14, 19) p e rep(1 6, 6) P 1- (9.14, .20, 0.13, 9.20, 9.13, 8.28) n_2 <-e(0.14, e.30, 8.13, 6.15, 0.13, 0.15) lik <-c(dmultinon( freq, lee, prob = P-B), dmultinom( freq, lee, prob p-1),dnultinon( freq, 100, prob P-2)) : Suppose we assign prior probabilities P(Fair) - 0.1, P(Bias0.45 and P(Bias2) - 0.45 (a) What s the posterior probabilty for Fair? Answer to four significant figures. (b) What is the posterior probability for Bias,? Answer to four significant figures. (c) What is the posterior probability for Bias2? Answer to four significant figures. The joint distribution of X and Y is given in the tollowing table Face Value Fair model 1/6 1/6 1/6 1/61/6 1/6 Blased model I 0.14 0.20 0.13 0.200.13 0.20 Biased model 11: | 0.14 | 0.30 0.13 1st 100 rolls: 2nd 100 rolls: 14 20 15 19 20 19 19 19 13 Table 1: Probabilities and likelihoods for the three models considered in number 1. The last two rows show the observed frequencies among the first 100 rolls and the second 100 rolls, respectively

Answer 1