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an insurer receives independent claims of the same law of probability of E(X)=10 and standard deviation 2 in thousands of dollars according to a process of poisson in continuous time of intensity 1 per day. Using an approximation by a normal distribution, calculate: (a) the probability that the 100th claim of the year arrives during the 90 first days of the year, ie before the start of April 1; (b) the probability that the average amount of the first 100 claims of the year is over $ 10.5 thousand.

an insurer receives independent claims of the same law of probability of E(X)=10 and standard deviation 2 in thousands of dollars according to a process of poisson in continuous time of intensity 1 per day. Using an approximation by a normal distribution, calculate: (a) the probability that the 100th claim of the year arrives during the 90 first days of the year, ie before the start of April 1; (b) the probability that the average amount of the first 100 claims of the year is over $ 10.5 thousand.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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an insurer receives independent claims of the same law of probability of E(X)=10 and standard deviation 2 in thousands of dollars according to a process of poisson in continuous time of intensity 1 per day. Using an approximation by a normal distribution, calculate: (a) the probability that the 10Oth claim of the year arrives during the 90 first days of the year, ie before the start of April 1; (b) the probability that the average amount of the first 100 claims of the year is over $ 10.5 thousand.
Transcribed Image Text:an insurer receives independent claims of the same law of probability of E(X)=10 and standard deviation 2 in thousands of dollars according to a process of poisson in continuous time of intensity 1 per day. Using an approximation by a normal distribution, calculate: (a) the probability that the 10Oth claim of the year arrives during the 90 first days of the year, ie before the start of April 1; (b) the probability that the average amount of the first 100 claims of the year is over $ 10.5 thousand.
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