It is said that the number of traffic accidents in Sinchon Rotary follows the Poisson distribution, of which the expected value is three times per hour. When the number of traffic accidents in the Sinchon Rotary during the 30 days independent of each other is X1, X2, ..., X30, answer the following questions. (1) The random variable Y is the sum of the number of traffic accidents in the Sinchon Rotary for 30 days independent of each other. Find the distribution of Y. (e.g. normal distribution, binomial distribution, etc.) (2) Use (1) to calculate the probability that the time until two traffic accidents occur in 30 days exceeds 20 hours. (3) For three years, Mike had never seen a traffic accident while traveling the Sinchon Rotary almost every day, so he usually thought that the number of traffic accidents would be less than three per hour. To confirm this, A surveyed the number of traffic accidents at Sinchon Rotary for one hour for 30 days, and as a result, the average number of incidents was 2.6 and the standard deviation for 30 days was 1.5. Based on this survey, examine whether the number of traffic accidents per hour of Sinchon Rotary can be deemed to be less than three with 5% level of significance.
It is said that the number of traffic accidents in Sinchon Rotary follows the Poisson distribution, of which the expected value is three times per hour. When the number of traffic accidents in the Sinchon Rotary during the 30 days independent of each other is X1, X2, ..., X30, answer the following questions. (1) The random variable Y is the sum of the number of traffic accidents in the Sinchon Rotary for 30 days independent of each other. Find the distribution of Y. (e.g. normal distribution, binomial distribution, etc.) (2) Use (1) to calculate the probability that the time until two traffic accidents occur in 30 days exceeds 20 hours. (3) For three years, Mike had never seen a traffic accident while traveling the Sinchon Rotary almost every day, so he usually thought that the number of traffic accidents would be less than three per hour. To confirm this, A surveyed the number of traffic accidents at Sinchon Rotary for one hour for 30 days, and as a result, the average number of incidents was 2.6 and the standard deviation for 30 days was 1.5. Based on this survey, examine whether the number of traffic accidents per hour of Sinchon Rotary can be deemed to be less than three with 5% level of significance.
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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Transcribed Image Text:It is said that the number of traffic accidents in Sinchon Rotary follows the Poisson distribution, of which the expected value is
three times per hour. When the number of traffic accidents in the Sinchon Rotary during the 30 days independent of each other
is X1, X2, ..., X30, answer the following questions.
(1) The random variable Y is the sum of the number of traffic accidents in the Sinchon Rotary for 30 days independent of each
other. Find the distribution of Y. (e.g. normal distribution, binomial distribution, etc.)
(2) Use (1) to calculate the probability that the time until two traffic accidents occur in 30 days exceeds 20 hours.
(3) For three years, Mike had never seen a traffic accident while traveling the Sinchon Rotary almost every day, so he usually
thought that the number of traffic accidents would be less than three per hour. To confirm this, A surveyed the number of
traffic accidents at Sinchon Rotary for one hour for 30 days, and as a result, the average number of incidents was 2.6 and the
standard deviation for 30 days was 1.5. Based on this survey, examine whether the number of traffic accidents per hour of
Sinchon Rotary can be deemed to be less than three with 5% level of significance.
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