here's my question

1. Let X be binomial(5, 0), where 0 S 0 g 1 is unknown. Using the Bayesian approach, we model 9 with a random variable 8. Suppose researchers who are interested in knowing 9 have already established that it is very likely that 9 is close to 1 and not likely that 0 is close to O. (a) (4 points) Out of the following densities, which of the following density is the best choice of prior for 8? (i) 13(0) = 1 for 0 g 0 g 1; (ii) 13(9) = 29 for 0 g 9 g 1; (iii) f3(6) = e9 for o g 6. Explain your answer. (b) (8 points) Let f9 (0) be the prior density you chose in part (a). Suppose we observe X = 5. Given this observation, nd the posterior density 6. (c) (4 points) Between the prior and posterior densities of 8 in part (b), which has more density near 1? Explain the intuition of Why the density you identify should have more density near 1