Question

Can you please show a few iterations so I can try and figure out the math behind this instead of just the answers? I would really appreciate it.

Data on the following slide are the vehicle arrival times at a stop sign. The total time span of the recording was T = 240 minutes. - What is the average rate l? - Calculate the interarrival times. - Provide visual matches of the data vs. Poisson and data vs. Expo. Use 1-min intervals for the Expo interarrival times Use 10-min intervals for the Poisson [use Excel or any software you like or you can also do it manually]

7.0 78.3 137.7 202.4 25.0 80.7 141.8 208.2 26.1 86.6 142.3 212.2 26.4 88.7 148.8 214.9 26.9 90.2 152.6 215.1 26.9 90.8 165.9 228.2 33.8 95.2 167.0 233.9 45.1 108.3 168.3 234.8 47.1 124.9 173.8 235.0 47.6 130.7 178.8 235.5 57.3 136.3 196.8 238.0

Answer 1

Data on the following slide are the vehicle arrival times at a stop sign The total time span of the recording was T-240 minutes. The average rate is, sum of observations/total number of observations. 5711.9 129.81 The Inter arrival time is difference between arrival times. 25 26.1 26.4 26.9 26.9 33.8 45.1 47.1 47.6 57.3 78.3 80.7 86.6 88.7 18 1.1 0.3 0.5 6.9 11.3 0.5 9.7 2.4 5.9

For example: 25-7-18 26.1 25 1.1 26.4-26.1 = 0.3 etc Let X be the arrival time at a stop sign. X ~ Poisson (λ 129.81) And let Y be the inter arrival time. Y follows Exponential distribution. Use 1-minute for the exponential inter arrival times. That is the width of the class interval is 1 Minimum of the inter arrival time is 0 and maximum of the inter arrival time is 21 So the first class is 0-1 second class is 0-2 and so on...

classes frequency classes frequency 0--1 1--2 2--3 3--4 4--5 5--6 6--7 7--8 8--9 9--10 10--11 10 10--11 11--12 12--13 13--14 14--15 15--16 16--17 17--18 18--19 19--20 20--21 total 0 0 43

Use 10 minutes intervals for the Poisson. Minimum of the arrival time is 7 Maximum of the arrival time is 238. frequency frequencyclass 137--147 147--157 157--167 167--177 217--227 177-187 187--197 97--207 17--27 27--37 37--47 47-57 57--67 67-77 77--87 87-97 97--107 107-117 117-127 127-137 2 207--217 217--227 227--237 237--247 43
thank you