Rolling dice Let + be the outcome of rolling a six-faced die once, taking values in the set D :- {0.090.8,0). We denote the probability of observing a specific die face [ by p(x - D) - . The die could be loaded (unfair), yet these probabilities are still subject to the usual constraints V- D: 1 20. and Ex- 1. O-D Rolling the die / times in a row, we collect observations X - {,);) .. with each 4: c (0,0,6,0.5 0} (a) Give the joint probability of observing X, pix I ), and briefly explain your assumptions. (bi State the maximum likelihood problem for learning optimal I given observed X. Make sure to address the partition of unity constraint (Unep * - 1) but disregard non-negativity