Let x be the outcome of rolling a six-faced die once, taking values in the set D := {0,0,0,0,@), B). We denote the probability of observing a specific die face O by p(x =0) = ]. The die could be loaded (unfair), yet these probabilities are still subject to the usual constraints VOED: 120, and DED Rolling the die / times in a row, we collect observations X = {x, ) , with each x, c {0,0,0,0,8,0}. (a) Give the joint probability of observing X, p(X | It), and briefly explain your assumptions. (b) State the maximum likelihood problem for learning optimal * given observed X. Make sure to address the partition of unity constraint (Zep t - 1), but disregard non-negativity.(c) Solve the maximum likelihood problem. (We denote by N the number of times ( was seen. Show your work.)