Problem 2To go to the math department, a student takes the 49 bus, then the 68, or can decide for each busride to bike instead. At the end of the day, the student makes four trips (two to get to UBC, andtwo to get home using the same route), and decides to plan their next day by picking one of thetrips uniformly at random, and use the alternative way of transport (if it was a bus ride, then thestudent will bike and vice versa). Let Xn 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 timedoes 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 oftransport, the student takes the bus to UBC and bikes home on the next day. Let Y, be the numberof 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 Yn. Is the process reversible? Justify.18

Answered: To go to the math department, a student…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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