Let N be the number of insurance claims per year, and N is following a Poisson distribution, with a rate of X = 10000 year. We are interested in the probability that the number of insurance claims per year is larger than 10200. 1. Write down the equation to calculate the probability P(N > 10200). 2. Explain with it is undesirable to calculate this without software or approximations. 3. Use R to calculated P(N> 10200). 4. Write the equation of the normal approximation of this Poisson distribution and calculate P(N> 10200). You may use R to calculate cdf or pdf for the Normal distribution. 5. Comment on the approximation of the Poisson-distribution with a Normal-distribution.
Let N be the number of insurance claims per year, and N is following a Poisson distribution, with a rate of X = 10000 year. We are interested in the probability that the number of insurance claims per year is larger than 10200. 1. Write down the equation to calculate the probability P(N > 10200). 2. Explain with it is undesirable to calculate this without software or approximations. 3. Use R to calculated P(N> 10200). 4. Write the equation of the normal approximation of this Poisson distribution and calculate P(N> 10200). You may use R to calculate cdf or pdf for the Normal distribution. 5. Comment on the approximation of the Poisson-distribution with a Normal-distribution.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let N be the number of insurance claims per year, and N is following a Poisson distribution, with a rate of
A = 10000 year. We are interested in the probability that the number of insurance claims per year is larger
than 10200.
1. Write down the equation to calculate the probability P(N > 10200).
2. Explain with it is undesirable to calculate this without software or approximations.
3. Use R to calculated P(N> 10200).
4. Write the equation of the normal approximation of this Poisson distribution and calculate P(N > 10200).
You may use R. to calculate cdf or pdf for the Normal distribution.
5. Comment on the approximation of the Poisson-distribution with a Normal-distribution.
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