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To go to the math department, a student takes the 49 bus, then the 68, or can decide for each bus ride to bike instead. At the end of the day, the student makes four trips (two to get to UBC, and two to get home using the same route), and decides to plan their next day by picking one of the trips uniformly at random, and use the alternative way of transport (if it was a bus ride, then the student will bike and vice versa). Let X,, be the number of bus rides made on day n. a. Draw the transition diagram associated with this process. b. Show that the distribution (1,4, 6, 4, 1) is stationary, and that the process is reversible. What distribution do you recognize here? c. Suppose each bus trip takes 20 minutes and a bike trip 24. In the long run, how much time does the student spend on average to get from home to UBC? (justify your answer) d. The student decides to modify their strategy: if all the trips were made using the same mode of transport, the student takes the bus to UBC and bikes home on the next day. Let Y,, be the number of bus rides made during the n-th day for the modified process. Draw the transition diagram. e. We assume that o=(1,4,8, 4, 1) is stationary for Y₁. Is the process reversible? Justify.

To go to the math department, a student takes the 49 bus, then the 68, or can decide for each bus ride to bike instead. At the end of the day, the student makes four trips (two to get to UBC, and two to get home using the same route), and decides to plan their next day by picking one of the trips uniformly at random, and use the alternative way of transport (if it was a bus ride, then the student will bike and vice versa). Let X,, be the number of bus rides made on day n. a. Draw the transition diagram associated with this process. b. Show that the distribution (1,4, 6, 4, 1) is stationary, and that the process is reversible. What distribution do you recognize here? c. Suppose each bus trip takes 20 minutes and a bike trip 24. In the long run, how much time does the student spend on average to get from home to UBC? (justify your answer) d. The student decides to modify their strategy: if all the trips were made using the same mode of transport, the student takes the bus to UBC and bikes home on the next day. Let Y,, be the number of bus rides made during the n-th day for the modified process. Draw the transition diagram. e. We assume that o=(1,4,8, 4, 1) is stationary for Y₁. Is the process reversible? Justify.

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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To go to the math department, a student takes the 49 bus, then the 68, or can decide for each bus ride to bike instead. At the end of the day, the student makes four trips (two to get to UBC, and two to get home using the same route), and decides to plan their next day by picking one of the trips uniformly at random, and use the alternative way of transport (if it was a bus ride, then the student will bike and vice versa). Let X₁, be the number of bus rides made on day n. a. Draw the transition diagram associated with this process. b. Show that the distribution = (1,4, 6, 4, 1) is stationary, and that the process is reversible. What distribution do you recognize here? c. Suppose each bus trip takes 20 minutes and a bike trip 24. In the long run, how much time does the student spend on average to get from home to UBC? (justify your answer) d. The student decides to modify their strategy: if all the trips were made using the same mode of transport, the student takes the bus to UBC and bikes home on the next day. Let Y,, be the number of bus rides made during the n-th day for the modified process. Draw the transition diagram. e. We assume that a = (1,4,8, 4, 1) is stationary for Y₁. Is the process reversible? Justify.
Transcribed Image Text:To go to the math department, a student takes the 49 bus, then the 68, or can decide for each bus ride to bike instead. At the end of the day, the student makes four trips (two to get to UBC, and two to get home using the same route), and decides to plan their next day by picking one of the trips uniformly at random, and use the alternative way of transport (if it was a bus ride, then the student will bike and vice versa). Let X₁, be the number of bus rides made on day n. a. Draw the transition diagram associated with this process. b. Show that the distribution = (1,4, 6, 4, 1) is stationary, and that the process is reversible. What distribution do you recognize here? c. Suppose each bus trip takes 20 minutes and a bike trip 24. In the long run, how much time does the student spend on average to get from home to UBC? (justify your answer) d. The student decides to modify their strategy: if all the trips were made using the same mode of transport, the student takes the bus to UBC and bikes home on the next day. Let Y,, be the number of bus rides made during the n-th day for the modified process. Draw the transition diagram. e. We assume that a = (1,4,8, 4, 1) is stationary for Y₁. Is the process reversible? Justify.
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