A jar contains halls of three different colors, with the fraction of red, green and blue being (91,32,33) respectively. Assume that 91 = $92 = 7}, + g and 93 = % g, where 9r is the parameter we wish to know. A man draws N balls from the jar with replacement, in which the number of red, green and blue balls are (n1, n2, n3) respectively. Unfortunately, the person who is doing the experiment is actually colorblind and cannot discern red from green, therefore he only sees m1 2 m + H2 red/green balls and m2 = R3 blue balls. Can the person still estimate the parameter 7r, as well as calculating his best guess for the number of red and green balls? For this question, assume a uniform prior on 7r. Work through the following steps to nd out. b) Identify the posterior distribution of H1 given m1 and 91', specifying its mean and variance