Suppose that Y is binomially distributed Y ~ Bin(n = 5,0) where O is unknown. Furthermore, assume that 0 E O = (0.0, 0.1,..., 0.9, 1.0), and that a priori we view each of these 11 possibilities as equally likely, i.e. P(0) = 11 for each 0 E O. (a) Using the Bayes' rule, write down a formula for the posterior distribution P(0 | y) in terms of 0;, and simplify as much as possible. (b) For y = 0, make a plot for P(0 | y) for each 0 E O = (0.0, 0.1,...,0.9, 1.0). In other words, make a plot with the horizontal axis representing the 11 values of O and the vertical axis representing the corresponding values of P(0 | y). (c) Repeat (b) for each y E {1, 2, 3,4,5), so in the end you have six plots (including the one in (b)). Describe what you see in your plots and discuss whether or not they make sense