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17: Start with the Poisson distribution: Pm = 'ule\". m. a: Verify that Z Pm = 1. Hint: don't forget the series expansion for e\". o b: Show that m = ,u. : np. Hint: you have to rewrite the series. m a m c: Show that the standard deviation is . Hint: mg'u = a$( . m! m! 18: A radioactive source emits 200 a particles in 100 minutes. Assume that its average rate of emission was constant for that 100 minutes. Use the Poisson distribution to determine the probability that a particular minute had 0, 1, 2, 3, 4, 5, or 6 emissions. Approximately graph the result. 19: 520 people each randomly select one card from their own decks of 52 cards. a: Use the binomial distribution to determine the probability that 13 people select the ace of spades. b: Would you expect the Gaussian or Poisson Distribution to be a better approximation in this case? Explain. c: Use the Gaussian and Poisson Distributions to approximate the probability. Was your expectation correct