6. The Hayward campus has become a dangerous place for people on motorized scooters. Thereare six intersections on the campus loop, independent of one another, for which accidents occurfollowing a Poisson process with different rates, say A₁,..., A6, per week. The Board of CampusSafety is interested in the total number of accidents that occur next semester (sixteen weeks).(a) Using the moment generating function, derive the distribution of the total number ofaccidents that occur next semester at these intersections combined. Make sure you defineall variables used.(b) Suppose, from past experience, it is known that the values of A₁,..., A6 are 0.8, 1.2, 2.9,0.2, 1.1, and 2.8 respectively. What is the probability that there are between 142 and 146(inclusively) accidents on the campus loop next semester?(c) What is the expected value and standard deviation for the number of accidents on thecampus loop next quarter?

Answered: Image /qna-images/answer/c43987dd-d91a-4f61-8670-0673b23ac477.jpg

Answered: The Hayward campus has become a…

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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Imagine that a professor of psychology has two teaching assistants (TAs) who will help her grade assignments for the duration of the semester. The professor wants to make sure that she and the TAs are well calibrated with one another, so she has all three of them grade the first assignment independently. Because the professor grades every assignment on a curve, she first converts the students’ scores to z-scores for each grader. The following table shows the z-scores for a population of 10 students in her class for each grader. Professor Teaching Assistant #1 Teaching Assistant #2 Student 1 0.70 1.27 1.27 Student 2 0.83 -0.64 -1.55 Student 3 -0.98 0.38 -0.14 Student 4 2.21 0.80 0.92 Student 5 -0.54 -1.34 -1.06 Student 6 0.43 0.10 0.30 Student 7 -1.03 -2.09 -1.50 Student 8 -0.01 0.85 1.14 Student 9 -0.54 0.48 0.57 Student 10 -1.07 0.20 0.04 The professor is going to use the z-scores to calculate the correlation coefficient between her scores…
You set up a series of cameras along the Mexican border. The rate of appearances of Jaguars is 4/18 years. Your cameras also produce pictures of wolf-sized canids, either wolves or coy-wolves in the same region. Each year your cameras catch about 400 of these animals, about 60 cougars and about 700 bears and 1200 feral hogs. Assume that these numbers are all population rates for Poisson. Given your cameras catch a non human large animal (and the above list is all of them): i. What is the probability it is a jaguar? (Hint: Animals are independent. This is asking the conditional probability of a jaguar, given you see an animal) ii. What is the probability it is a feral hog? iii. Out of 25 large nonhuman animals, what is the probability that 15 or more are feral hogs? (Hint N=25, P is fixed, independent trials) iv. Out of 180 large non human animals what is the probability that between 100 and 170 are feral hogs?
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The following table shows the typical depth (rounded to the nearest foot) for nonfailed wells in geological formations in Baltimore County (The Journal of Data Science, 2009, Vol. 7, pp. 111-127). Geological Formation Group Number of Nonfailed Wells Nonfailed Well Depth Gneiss 1,515 255 Granite 26 218 Loch Raven Schist 3,290 317 Mafic 349 231 Marble 280 267 Prettyboy Schist 1,343 255 Other schists 887 267 Serpentine 36 217 Total 7,726 2,027 Let the random variable X denote the depth (rounded to the nearest foot) for nonfailed wells. Detemine the cumulative distribution function for X. Round your answers to four decimal places (e.g. 98.7654). x < 217 217
EXAMPLE 6.16 A self-service store employs one cashier at its counter. Nine customers arrive on an average 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find (i) the average number of customers in the system, (ii) the average number of customers in queue or average queue length, (iii) the average time a customer waits before being served, and (iv) the average time a customer spends in the system.
Matthew the Barber owns a one-chair shop. At barber college, they told Matthew that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Matthew an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Part (b): The average time a customer waits. Part (c): The average time a customer is in the shop. Part (d): The average utilization of Matthew's time.
A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of five per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. a. Calculate the percentage utilization of the graduate student. (Round your answer to 1 decimal place.) b. Calculate the average number of students in the system, including the graduate student service desk. (Round your answer to 1 decimal place.) c. Calculate the average time in the system. (Round your answer to 1 decimal place.) d. Calculate the probability of four or more students being in line or being served. (Round your intermediate calculations to 3 decimal places and final answer to…
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a. A researcher studied the effect of social influence on drinking behaviour. Sixty people were randomly assigned to one of three conditions where they were given a soft drink to consume while waiting for the experiment to supposedly begin. An experimental assistant, posing as another participant, was also given a drink. In one condition, the assistant sipped the drink at a faster rate than the research participant; in another condition, the assistant sipped the drink at the same rate as the participant; and in the last condition, the assistant sipped the drink at a slower rate than the participant. The time it took each participant to consume his or her drink was measured.
What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. x 16.1 26.3 29.2 38.3 51.3 20.5 22.7 y 2.68 1.98 1.48 1.03 0.75 2.38 2.20 (b) Use a 1% level of significance to test the claim that ? < 0. (Round your answers to two decimal places.) t = critical t =
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