= 2. 16+6+6 18 pts] (Probability) Suppose that m balls are thrown into n bins at random. So, each time a ball is thrown, every bin is equally likely to get it. (i) Let Z be the number of balls that are thrown into bin 1. What are the possible values that Z can take? Write down the probability distribution for Z. (ii) Let X, be the random variable defined by X if bin 1 gets exactly one ball, 0 otherwise. Write down the probability distribution for X, and calculate E(X₁). (iii) Let X be the random variable that equals the number of bins that get exactly 1 ball. Find E(X). Justify each step of your argument.