Example 1 (discrete data)• 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

Example 2 (continuous data)• 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

Example 3 (parameter estimation)• 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

Example 4• A robot 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

Example 5• The rates 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

example 6 (chi-square test)• 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

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 6Frequency of occurrence 35 40 13 6 4 1 1