A. For the chi-squared test of independence between two categorical variables, we use the fact that the MLE for the probability that a multinomial trial is of category i is ni /n, where ni is the number of trials that fall into category i, and n is the total number of trials. Prove the previously stated fact.

b. Explain how two independent multinomial experiments, denoted as E1 and E2, can actually be thought of as a single multinomial experiment, denoted as E. In particular: i) How does the number of categories of E relate to the number of categories in E1 and E2? ii) Additionally, how do the category probabilities of E relate to the category probabilities of E1 and E2?