1. (Poisson Approximation). There are five coins on a desk, with probabilities .05, .1, .05, .01, and .04 for heads. Using a Poisson approximation, find the probability of obtaining at least one head when the five coins are each tossed once. Is the number of heads obtained binomially distributed in this problem?
2. (Poisson Approximation). Typically, about 6% of guests with a confirmed reservation at a hotel with 1100 rooms do not show up. During a convention, the hotel is already completely booked. How many additional reservations can the hotel grant and be 99% sure that the number of guests with a confirmed reservation who will be denied a room is at most two?
3. (Use Your Computer). Simulate the birthday problem to find the first person with the same birthday as yours. Perform the simulation 500 times. How many people did it take to find the first match? Was it typically about the same as the theoretical expected value?