The occurrence of traffic accidents at an intersection may be modeled as a Poisson process. Based onhistorical records the average rate of accidents is once every 6 years.Part 1What is the probability that there will be no accidents at the intersection for a period of 3 years?(Answer correct to 3 decimal places.)number (rtol=0.001, atol=D0.001)Part 2Suppose that in every accident at the intersection, there is a 5% probability of fatality. Based on theabove Poisson model what is the probability of one traffic fatality at this intersection in a period of 3years? (Answer correct to 3 decimal places.)Hint: Note that here you need to find the mean rate of fatalities per year, first.number (rtol=0.001, atol=D0.001)

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Answered: The occurrence of traffic accidents at…

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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Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. An Internet advertising agency is studying the number of "hits" on a certain web site during an advertising campaign. It is hoped that as the campaign progresses, the number of hits on the web site will also increase in a predictable way from one day to the next. For 10 days of the campaign, the number of hits × 105 is shown. Original Time Series Day 1 2 3 4 5 6 7 8 9 10 Hits × 105 1.3 3.5 4.4 7.2 6.8 8.3 9.0 11.3 13.1 14.7 Test ρ > 0 at the 1% level of significance. (Use 2 decimal places.) t
Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar.A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year 1 2 3 4 5 6 7 $ per capita 32.27 34.06 37.83 43.32 44.62 49.67 51.83 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data…
The manager of a gas station has observed that the times required by drivers to fill their car's tank and pay are quite variable. In fact, the times are exponentially distributed with a mean of 6.5 minutes. What is the probability that a car can complete the transaction in less than 6 minutes?
4
Roll two fair dice. Use the Poisson approximation to find the probability that you will rollat least one double (meaning both dice land on the same value) in 24 trials. How does this compare tothe exact value? Answer as if explaining to someone.
The time between failures of our video streaming service follows an exponential distribution with a mean of 40 days. Our servers have been running for 17 days, What is the probability that they will run for at least 97 days? (clarification: run for at least another 80 days given that they have been running 17 days). Report your answer to 3 decimal places.
The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?
6. True or False? Assume the below life table was constructed from following individuals who were diagnosed with slow-progressing form of prostate cancer and decided not to receive treatment of any form. The calculated survival probability for year 3, if the Kaplan-Meir approach is used to calculate the survival probability, is approximately 0.7438. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1
indicate the units to the final answer if any Draw the necessary graph if any. Round off to four decimal places or in lowest term if your answer is in fraction.
(c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?
Please solve (b) only!
Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. A research veterinarian at a major university has developed a new vaccine to protect horses from West Nile virus. An important question is: How predictable is the buildup of antibodies in the horse's blood after the vaccination is given? A large random sample of horses were given the vaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8 weeks. Results are shown in the following time series. Original Time Series Week Buildup Factor 2 3 4…

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