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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).

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).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 27E
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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.
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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