Stastistics

1. Task Conduct manual fitting of the given data following the “Three Activities” discussed in the class. 
       Activity I: (1) Draw a proper plot to represent the data (e.g., histogram, line graph) and
                         (2)  hypothesize the distribution that may best fit the data.
        Activity II: Estimate parameter(s) using the maximum likelihood estimation method. (hint: the exponential distribution is usually used for representing the arrival patterns). 
      Activity III: Test the goodness of fit using the Chi-square test.
 2. Data The .txt file (attached) provides you one-hour arrival times and inter-arrival times collected previously at the Central Library. 
 o First column: # of arrivals. A total of 28 arrivals were observed during this one-hour period.
  o Second column: inter-arrival times. Each data point captured the inter-arrival time between the previous arrival and the current arrival.  
o Third column: actual arrival times
 3. Deliverable You are asked to submit a report that shows your work on this input data analysis (i.e., the three activities mentioned above). Please also describe the issues encountered and remedies for these issues during the data fitting process. In addition, adequate justification for the selection of  your final distribution must be provided 
Lap 28 00:02:39.66 01:01:13.82
Lap 27 00:00:00.73 00:58:34.16
Lap 26 00:01:39.09 00:58:33.42
Lap 25 00:01:22.02 00:56:54.33
Lap 24 00:00:07.78 00:55:32.31
Lap 23 00:04:05.04 00:55:24.52
Lap 22 00:01:43.40 00:51:19.47
Lap 21 00:00:58.37 00:49:36.07
Lap 20 00:02:34.54 00:48:37.70
Lap 19 00:10:57.16 00:46:03.16
Lap 18 00:01:42.32 00:35:06.00
Lap 17 00:00:14.85 00:33:23.67
Lap 16 00:01:51.73 00:33:08.81
Lap 15 00:02:22.52 00:31:17.07
Lap 14 00:00:00.92 00:28:54.55
Lap 13 00:00:09.30 00:28:53.62
Lap 12 00:06:06.19 00:28:44.32
Lap 11 00:00:54.67 00:22:38.13
Lap 10 00:00:33.37 00:21:43.45
Lap 9 00:01:50.97 00:21:10.07
Lap 8 00:00:03.99 00:19:19.10
Lap 7 00:00:09.06 00:19:15.10
Lap 6 00:01:57.24 00:19:06.03
Lap 5 00:10:53.77 00:17:08.79
Lap 4 00:02:42.63 00:06:15.01
Lap 3 00:03:23.43 00:03:32.38
Lap 2 00:00:06.91 00:00:08.94
Lap 1 00:00:02.03 00:00:02.03

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