Unit 6 input modeling problems

Unit 6 input modeling problems

• 1.
  Example 1 (discretedata) • The number of vehicles arriving at the network corner of an intersection in a 5 minutes period between 7 am and 7.05 am was monitored for 5 work days over a 20 week period. The following table shows the resulting data. Draw an histogram for it. Arrivals per period Frequency Arrivals per period frequency 0 12 6 7 1 10 7 5 2 19 8 5 3 17 9 3 4 10 10 3 5 8 11 1
• 2.
  Example 2 (continuousdata) • Life tests are performed on a random sample of electronic components at 1.5 times the nominal voltage and their life time in days was recorded.. Draw a histogram for the following data • 79.919, 3.081, 0.062, 1.961, 5.845, 3.027, 6.505, 0.021, 0.013, 0.123, 6.679, 59.899,1.192, 34.760, 5.009,18.387, 0.141,43.565, 24.420, 0.433, 144.695, 2.663, 17.969, 0.091, 9.003, 0.941, 0.878, 3.371, 2.157, 7.579, 0.624, 5.380, 3.148, 7.078, 23.960, 0.590, 1.928, 0.300, 0.002, 0.543, 7.004,31.764, 1.005, 1.147,0.219, 3.217, 14.382,1.008,2.336,4.562
• 3.
  Example 3 (parameterestimation) • The number of vehicles arriving at the network corner of an intersection in a 5 minutes period between 7 am and 7.05 am was monitored for 5 work days over a 20 week period. The following table shows the resulting data. Estimate the value of the parameters and also find S2 Arrivals per period Frequency Arrivals per period frequency 0 12 6 7 1 10 7 5 2 19 8 5 3 17 9 3 4 10 10 3 5 8 11 1
• 4.
  Example 4 • Arobot is used to install the doors on automobile are assembly line, it was thought that the installation times followed a normal distribution, the robot is capable of measuring installation times accurately. A sample of 20 installation times was automatically taken by the robot with the following results. • 99.79, 99.56, 100.17, 100.33, 100.26, 100.41, 99.98, 99.83, 100.23, 100.27, 100.02, 100.47, 99.55, 99.62, 99.65, 99.82, 99.96, 99.90, 100.06, 99.85
• 5.
  Example 5 • Therates of 10 investments in a portfolio are 18.8, 27.9, 21.0, 6.1, 37.4, 5.0, 22.9, 1.0, 3.1 and 8.3 percent. Estimate the parameters of lognormal model of these data
• 6.
  example 6 (chi-squaretest) • The number of vehicles arriving at the network corner of an intersection in a 5 minutes period between 7 am and 7.05 am was monitored for 5 work days over a 20 week period. The following table shows the resulting data and test whether the data follows a poisson distribution using chi-square test of goodness of fit. Arrivals per period Frequency Arrivals per period frequency 0 12 6 7 1 10 7 5 2 19 8 5 3 17 9 3 4 10 10 3 5 8 11 1
• 7.
  Example 7 (chi-square) •Records pertaining to the monthly number of jobs related injuries and an underground coal mine where beings studied by a federal agencies values for the past 100 months are as follows. Apply the chi- square test to thin data to test the hypothesis that the underlying distribution is poisson using chi-square test of goodness of fit. Injuries/month 0 1 2 3 4 5 6 Frequency of occurrence 35 40 13 6 4 1 1