Each team member should spend 5 minutes to read and prepare an initial solution

Question

Each team member should spend 5 minutes to read and prepare an initial solution to the assignment The team members should spend the remainder of the time to compare answers, discuss the differences and prepare a group answer to be turned in It is important that each member spend time to answer the question individually to have a meaningful group discussion of the problem Grading Criteria: Question Rubric Weight Possible answered Question answered correctly, indicating student understands the concept Question Formula or calculation Did not attempt or question answered All 2 contains errors

Explanation / Answer

Here,

0.75^ 2 = (3/4)^2 = 9/16 is the probability for delays in the next two periods; 0.5625

If the probability of not being in a deay state is p in two consecutive periods then we have,

p = 0.85p +(1-0.75)(1-p) = 0.85p + 0.25 - 0.25p

p = 0.60p + 0.25

0.40p = 0.25

p = 0.25/0.40 = 5/8 = 0.625

Check the probability of no delay in the next period is 0.625(0.85) + 0.375(0.25)

which is 0.625 as the probability of no delay.

There is no way traffic conditions figure to be the same in the middle of the night as they are at rush hour. So no,the assumption of constant transition probabilitities would not be the same at all times.

The Markov process is the two state system N for no delay and D for delay with transition probabilities. Starting with N 0.85 probability of staying in N and 0.15 probability of moving to state D. Starting with D there is 0.75 probability of staying in D and 0.25 probability of moving to state N.

These are no realistic for all times of the day--but might be fairly realistic during midday hours between the rush hours.

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