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Statistics Homework Solutions 80

# Statistics Homework Solutions 80 - 80 CHAPTER 4 7(a Let X...

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80 CHAPTER 4 7. (a) Let X be the number of messages received in one hour. Since the mean rate is 8 messages per hour, X Poisson 8 . P X 5 e 8 8 5 5! 0 0916 (b) Let X be the number of messages received in 1.5 hours. Since the mean rate is 8 messages per hour, X Poisson 12 . P X 10 e 12 12 10 10! 0 1048 (c) Let X be the number of messages received in one half hour. Since the mean rate is 8 messages per hour, X Poisson 4 . P X 3 P X 0 P X 1 P X 2 e 4 4 0 0! e 4 4 1 1! e 4 4 2 2! 0 018316 0 073263 0 14653 0 2381 9. (ii). Let X Bin n p where μ X np 3. Then σ 2 X np 1 p , which is less than 3 because 1 p 1. Now let Y have a Poisson distribution with mean 3. The variance of Y is also equal to 3, because the variance of a Poisson random variable is always equal to its mean. Therefore
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