6. (10 points) (Poisson Approximation) Line up 100 boxes. Given 500 balls, randomly throw a ball into one of the 100 boxes. Label the boxes n = 1, 2, 3, ... , 100. The surprising conclusion of this exercise is that there is a 50% chance of at least one of the 100 boxes is empty! a. Let Xn be 1 if the nth box is empty, and 0 if it contains at least one ball. Here, n = 1, 2, . . . , 100. The exact distribution of Xn is Bernoulli with probability of success b. Count the number of empty boxes with the random variable Y = _ Xn. The approximate distribution of Y is Poisson with mean c. The chance that Y not zero (that is, there is an empty box) is p =