1. Note that the fractions of cars returned are per day . 2. What will be the di
ID: 2961932 • Letter: 1
Question
1. Note that the fractions of cars returned are per day.
2. What will be the distribution of cars after 1 week (7 days), i.e., the following Monday?
3. What was the distribution of cars 1 day before the start (on a Sunday)?
4. Describe the distribution of the cars if this process continues indefinitely. (Use technology.)
5. Is there a distribution of cars that you could start with so that you would end the day with the same number of cars at each location as you started with? Explain.
Explanation / Answer
Cars rented From: Airport East West Returned to | .97 .05 .10 | Airport | .00 .90 .05 | East | .03 .05 .85 | West Monday Tuesday | 304 | | 307 | A | 48 | = | 48 | | 98 | | 95 | Monday Wednesday | 304 | | 310 | A A | 48 | = | 48 | | 98 | | 92 | Long Term distribution: Percentage Cars |0.735294 0.735294 0.735294 | | 74 % | | 331 | |0.0882353 0.0882353 0.0882353 | or | 9 % | or | 40 | |0.176471 0.176471 0.176471 | | 28 % | | 79 | A = {{ 0.97, 0.05, 0.10}, { 0.00, 0.90, 0.05}, { 0.03, 0.05, 0.85}}; B = {304,48,98} Do[ A = A.A, {i,1,10}];
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