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Stat310            Bivariate distributions


                               Hadley Wickham
Friday, 26 February 2010
1. Test
                 2. Example
                 3. CDF
                 4. Expectation
                 5. Conditional distributions
                 6. Correlation


Friday, 26 February 2010
Test



Friday, 26 February 2010
15




     10
 n




       5




                                             C        B        A
       0

                 10        15   20      25       30       35       40
                                     Grade
Friday, 26 February 2010
But, you can expect
a boost of about 10%
from your homeworks
  15




     10
 n




       5




                                     C           B        A
       0

                 10        15   20          25       30       35   40
                                         Grade
Friday, 26 February 2010
Test
                     It was a bit harder than I intended (Question
                     1 was supposed to be the easiest ☹). I
                     don’t curve, but I will provide opportunities
                     for you to improve your overall grade.
                     Extra credit this week worth 5 points - you
                     may redo one question from the exam.
                     Model answers will be posted after spring
                     break.


Friday, 26 February 2010
Example



Friday, 26 February 2010
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     70
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     60


                                       ●

     50                                                                                                                                                                                   type
                                       ●
                                                                                                                ●                                                                          ●     3pt
                                                                                                                                          ●               ●
                                       ●                                                                                                                                                   ●     driving layup
                                           ●
     40                                                                                                                                                                                    ●     hook
 y




                                                                                                    ●


                                                                                   ●
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                                                                                                                                                                                           ●     jump
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                                                                                                                                                                                           ●     layup
     30                                    ●
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                                                                                                                                                                                           ●     turnaround jump
                                ●  ●  ●    ●   ●   ●   ●       ●       ●   ●   ● ● ● ● ●    ● ●     ●   ●     ●     ●   ● ●   ●     ●   ●     ●   ●   ●   ● ●   ● ●   ●
                                 ● ●  ●    ●   ●       ●       ●   ●   ●   ●   ● ● ● ● ●    ●       ●   ●   ● ●     ● ● ● ●   ●       ● ●         ●   ●   ● ●   ● ●   ●
                                ●● ●  ●    ●           ●
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                                ●● ●  ●    ●   ●   ●   ●
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                      ● ●   ●   ●● ●  ●    ●   ●   ●   ●
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     20             ●
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                      ● ●             ●    ●       ●   ●
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     10         ●
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                    ● ● ●   ●   ● ● ● ●    ●   ●   ● ● ●       ● ●     ●   ●   ● ● ● ● ●    ● ●     ●   ●   ●   ●   ● ● ● ●   ●   ● ● ● ●     ●   ●   ●   ● ●   ● ● ● ● ●     ●   ● ●
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                    ● ● ●       ● ●   ●    ●   ●                                              ●             ●                                         ●           ● ●   ●     ●   ●
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                0                          10                                      20                                30                           40                               50
                                                                                                x
Friday, 26 February 2010
3pt                                  driving layup                                  hook
                                           ●
                                       ●       ●
                                                ●
     70                        ●   ●                  ●
                           ●                              ●
                               ●
     60
                    ●
     50                                        ●
                    ●                                 ●       ●
                    ●
                     ●
     40                          ●
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                         ●●●●●●●●●●●●●●●
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                         ●●●●●●●●●●●●●●●●
                          ●●●●●●●●●●● ●●
                            ●●●●●●●● ●
     30               ●●● ●●●●●
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                       ● ● ●
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     20         ●●●
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     10      ●●
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                                               ●


                                           jump                                      layup                             turnaround jump
 y




     70

     60

     50

     40

     30                         ● ● ●
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                                                                                                                                ●   ●
     20             ●●●●●● ● ●●●●●●●●●●●
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                    ●●●●●         ●● ●●●● ●   ●                                                                              ●●       ●●
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                                   ●                                            ●                                        ●● ● ● ●●●●●●
                                                                                                                          ●   ● ● ●
                                                                                                                              ●
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                  ● ●●●●●●●●●●●●●●●●●●●
                   ● ●●● ● ● ●●●●●●●●●● ●
                     ● ●    ●     ●●●● ●●●●●
                  ●●●●●●●●●●●●●●●●●●●●●●   ● ●●                                                                   ● ● ● ● ●●● ●●●●●●●●
                                                                                                                         ● ●●●● ● ●●●
                                                                                                                                       ●
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                  ●●●●●●●●●●●●●●●●●●●●●
                       ●●●●●●●●●●●               ●                                                                 ●●          ●   ●
                                                                                                                         ● ● ●●●●● ●●
                                                                                                                          ●● ●          ●
     10           ●●●●●●●●●●●●●●●●●●●●●●
                  ●●●●●●●●●●●●●●●●●●●●●
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                  ●●●●●●● ●          ●●●●●●●●●●
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                  ● ●
                   ● ●                       ● ● ●                                      ● ●                       ●


             0       10            20            30       40      50   0   10       20       30   40   50   0     10      20      30     40     50
                                                                                         x
Friday, 26 February 2010
3pt                                  driving layup                                  hook
                                           ●
                                       ●       ●
                                                ●
     70                        ●   ●                  ●
                           ●                              ●
                               ●
     60
                    ●
     50                                        ●
                    ●                                 ●       ●
                    ●
                     ●
     40                          ●
                              ●
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                               ●   ● ●
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     30               ●●● ●●●●●
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                       ● ● ●
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     20         ●●●
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     10      ●●
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                                               ●                                                                         ● ●●●●●●●●
                                                                                                                              ●●●
                                                                                                                            ●●●●●●
                                                                                                                             ●●●●●●
              ●●
              ●●
               ●                              ●●
                                              ● ●
                                               ●●
                                               ●                                         ●●●●
                                                                                          ●●●
                                                                                         ●●●
                                                                                          ●●                           ● ●●●● ●●● ●
                                                                                                                             ● ●●● ●
                                                                                                                              ●● ●●
                                                                                                                        ● ● ● ●
             ●●
              ●●
             ●●
              ●●                              ●●
                                               ●
                                              ●●
                                               ●                                         ● ●●
                                                                                         ● ●
                                                                                          ●                            ● ●●● ● ● ●
                                                                                                                          ●
              ●●
              ●●                              ●●
                                               ●


                                           jump                                      layup                             turnaround jump
 y




     70

     60

     50

     40

     30                         ● ● ●
                           ● ●●●●●●●●
                              ●●●● ●
                            ●●●●●●●●●●●
                                   ●
                         ●●●●●●●●●●●●
                            ●●●●●●●●● ●
                             ●●●●●●●●
                               ● ●●● ●
                       ●●●●●●●●●●●●●●●
                       ●●●●●● ●
                          ●● ●
                     ●●●●●●●●●●●●●●●●●
                                   ●     ●
                    ●●●●●●●●●●●●●●●●●●
                     ●●●●●●●●●●●●●●●●●
                      ●●●●●●●●●●●●●●●●
                        ●●●●●●●●●●●●●●
                    ●●●●●●● ●●●●●●●●●●
                                                                                                                                ●   ●
     20             ●●●●●● ● ●●●●●●●●●●●
                    ●●●●●●
                    ●●●●●●●●●●●●●●●●●● ●
                    ●●●●●         ●● ●●●● ●   ●                                                                              ●●       ●●
                   ●●●●●●●●●●●●●●●●●●●●
                    ●●●●●●●● ●● ●●●●●●●
                    ●●●●●●● ●●●●●●●●●●●●
                     ●●●●●●●●●●●●●●●●●●
                    ●●●●●●●●●●●●●●●●●●●
                                 ●●●
                                         ●●
                                         ●●●●●
                                                                                                                       ●
                                                                                                                    ● ●● ●     ●
                                                                                                                               ●     ●● ●
                                                                                                                                       ●
                  ●●●●●●●●●●●●●●●●●●●●●
                   ●● ●●● ●● ●●
                   ●●●●●●●● ●●●● ●●●●●●●
                                   ●                                            ●                                        ●● ● ● ●●●●●●
                                                                                                                          ●   ● ● ●
                                                                                                                              ●
                                                                                                                              ●●●● ● ●
                  ● ●●●●●●●●●●●●●●●●●●●
                   ● ●●● ● ● ●●●●●●●●●● ●
                     ● ●    ●     ●●●● ●●●●●
                  ●●●●●●●●●●●●●●●●●●●●●●   ● ●●                                                                   ● ● ● ● ●●● ●●●●●●●●
                                                                                                                         ● ●●●● ● ●●●
                                                                                                                                       ●
                   ●●●●●●●●●●●●●●●●●●●●
                  ●●●●●●●●●●●●●●●●●●●●●
                       ●●●●●●●●●●●               ●                                                                 ●●          ●   ●
                                                                                                                         ● ● ●●●●● ●●
                                                                                                                          ●● ●          ●
     10           ●●●●●●●●●●●●●●●●●●●●●●
                  ●●●●●●●●●●●●●●●●●●●●●
                   ●●● ●●●●●●●●●●● ●●●● ●
                     ●●● ●●●●●●●●●
                 ●●●●● ●●●●●
                  ●●●●●● ●●●● ●●●● ●●●●●●   ●●●●
                                            ●●●●●                                     ●●●
                                                                                       ●●●                           ●● ●●
                                                                                                                     ●     ●
                                                                                                                             ● ●   ●
                                                                                                                  ●●●●● ●●● ● ●●●●● ●●
                                                                                                                                ● ● ●●●●
                 ●●●●●●●●●●●
                  ●●●●●●● ●          ●●●●●●●●●●
                                      ●●●●●●●●●●                                      ●●●●
                                                                                       ●●●                       ●●       ●         ●●●
                 ●●●●●●●●● ●
                  ●●●●● ● ● ●
                  ●●● ●●● ●
                  ●●●●● ●
                  ●●●
                  ● ●
                                       ●●●●●●●●●
                                       ●●●●●●●●●
                                        ●●●●●●●●
                                         ● ●●●●●
                                             ●● ●●
                                              ●●                                     ●●●●
                                                                                      ●●●●
                                                                                      ● ●●
                                                                                       ●●●                      ● ● ●● ●●
                                                                                                                     ●●              ●●● ●
                                                                                                                                       ●
                                                                                                                                        ● ●●●
                  ● ●
                   ● ●                       ● ● ●                                      ● ●                       ●


             0       10            20            30       40      50   0   10       20       30   40   50   0     10      20      30     40     50
                                                                                         x
Friday, 26 February 2010
Marginal distribution of y
             140



             120



             100



             80
 ..count..




             60



             40



             20



               0

                           5   10   15   20   25   30
                                     y
Friday, 26 February 2010
Marginal distribution of x

             80




             60
 ..count..




             40




             20




             0

                           10   20       30   40
                                     x
Friday, 26 February 2010
Joint distribution of x and y
2114 jumps
  30                                                                                             ●               ●   ●
                                                                                    ●        ●           ●   ●   ●   ●
                                                                        ●               ●    ●   ●   ●       ●   ●   ●       ●   ●            ●
                                                                            ●   ●       ●    ●   ●       ●   ●   ●   ●       ●   ●    ●   ●   ●   ●
                                                                ●       ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●       ●   ●        ●   ●   ●       ●       ●

     25                                                 ●       ●   ●   ●   ●   ●   ●   ●    ●   ●   ●       ●   ●   ●   ●   ●   ●    ●   ●   ●           ●   ●
                                                        ●   ●   ●   ●   ●   ●   ●   ●   ●        ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●
                                           ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●       ●   ●
                                       ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●       ●   ●   ●   ●   ●   ●   ●        ●   ●   ●   ●   ●   ●   ●   ●   ●    ●
                                   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●       ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●

     20                            ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●                    ●   ●   ●   ●   ●           ●        ●   ●   ●   ●   ●       ●   ●   ●    ●
                                   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●       ●    ●   ●   ●       ●   ●   ●   ●       ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●
                               ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●        ●   ●   ●   ●   ●           ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●           ●
                                       ●   ●        ●   ●   ●   ●   ●       ●   ●   ●   ●        ●   ●   ●   ●   ●   ●   ●       ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●       ●
                               ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●       ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●        ●   ●   ●   ●   ●       ●   ●   ●    ●   ●   ●   ●
 y




     15                    ●   ●       ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●        ●   ●   ●   ●   ●   ●   ●   ●   ●        ●       ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●
                           ●   ●       ●   ●   ●    ●   ●   ●           ●   ●   ●   ●   ●    ●       ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●
                           ●       ●       ●   ●    ●   ●   ●   ●   ●   ●   ●       ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●       ●   ●   ●
                           ●   ●           ●        ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●       ●   ●   ●   ●   ●    ●   ●       ●   ●       ●
                               ●   ●   ●   ●   ●            ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●       ●       ●   ●   ●   ●    ●   ●   ●       ●

     10               ●    ●   ●   ●   ●   ●        ●   ●   ●       ●   ●       ●   ●   ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●       ●   ●   ●   ●   ●   ●    ●   ●   ●           ●
                  ●   ●    ●   ●   ●   ●   ●   ●    ●       ●   ●       ●   ●   ●   ●   ●    ●   ●   ●   ●       ●   ●   ●   ●   ●        ●   ●   ●       ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●
                  ●   ●    ●   ●   ●   ●   ●   ●    ●   ●       ●   ●   ●   ●   ●   ●   ●        ●   ●                   ●   ●   ●    ●   ●   ●   ●       ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●
                      ●    ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●       ●        ●   ●                               ●    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●
                  ●   ●    ●   ●   ●   ●   ●   ●    ●   ●   ●       ●   ●   ●       ●            ●                                    ●   ●   ●   ●   ●   ●   ●   ●   ●   ●    ●   ●   ●   ●   ●   ●   ●

       5              ●    ●   ●       ●   ●        ●   ●   ●       ●               ●                                                                     ●       ●   ●        ●       ●   ●   ●   ●
                           ●   ●       ●   ●   ●                                                                                                                          ●                ●   ●
                                           ●                                                                                                                      ●            ●



                                               10                                       20                                       30                                       40



                                                                                                         x
Friday, 26 February 2010
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate
13 Bivariate

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13 Bivariate

  • 1. Stat310 Bivariate distributions Hadley Wickham Friday, 26 February 2010
  • 2. 1. Test 2. Example 3. CDF 4. Expectation 5. Conditional distributions 6. Correlation Friday, 26 February 2010
  • 4. 15 10 n 5 C B A 0 10 15 20 25 30 35 40 Grade Friday, 26 February 2010
  • 5. But, you can expect a boost of about 10% from your homeworks 15 10 n 5 C B A 0 10 15 20 25 30 35 40 Grade Friday, 26 February 2010
  • 6. Test It was a bit harder than I intended (Question 1 was supposed to be the easiest ☹). I don’t curve, but I will provide opportunities for you to improve your overall grade. Extra credit this week worth 5 points - you may redo one question from the exam. Model answers will be posted after spring break. Friday, 26 February 2010
  • 8. ● ● ● 70 ● ● ● ● ● ● 60 ● 50 type ● ● ● 3pt ● ● ● ● driving layup ● 40 ● hook y ● ● ● ● ● jump ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● layup 30 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● turnaround jump ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 20 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0 10 20 30 40 50 x Friday, 26 February 2010
  • 9. 3pt driving layup hook ● ● ● ● 70 ● ● ● ● ● ● 60 ● 50 ● ● ● ● ● ● 40 ● ● ●●● ●● ● ● ● ●●●●●●●●●●●●●●● ●●●● ●●● ●●●●●●●●●●●●●●●● ● ●●●●●●●●●●●●●●●● ●●●●●●●●●●● ●● ●●●●●●●● ● 30 ●●● ●●●●● ●●●● ● ●● ●●●●●●● ● ● ● ●●●●●● ●●●●●● ●●●●● ●●● ●●● ●●●●●● ●●●●● ●●●●● ●●●●● ●●●● ●●●● ●●● ●●● ●● ●●●● ●●●● ●●●● ●●●● ●●● ●● ●●● ●● ●●● ●●● ●●● ●●● ●●●● ● ●●●● ●●● 20 ●●● ●●●● ● ●●● ●●● ●● ●● ●● ●● ●● ● ●● ●● ● ● ● ● ● ●● ●●● ●●●●●●● ●● ● ● ●● ● ●● ● ●●●● ● ●● ● ●●●●● ● ● ●● ● ●● ● ●● ●● ● ● ● ●● ● ● ●●●●●●● ● ● 10 ●● ●● ●● ● ● ●● ●● ●●● ● ● ●●●●●●●● ●●● ●●●●●● ●●●●●● ●● ●● ● ●● ● ● ●● ● ●●●● ●●● ●●● ●● ● ●●●● ●●● ● ● ●●● ● ●● ●● ● ● ● ● ●● ●● ●● ●● ●● ● ●● ● ● ●● ● ● ● ● ●●● ● ● ● ● ●● ●● ●● ● jump layup turnaround jump y 70 60 50 40 30 ● ● ● ● ●●●●●●●● ●●●● ● ●●●●●●●●●●● ● ●●●●●●●●●●●● ●●●●●●●●● ● ●●●●●●●● ● ●●● ● ●●●●●●●●●●●●●●● ●●●●●● ● ●● ● ●●●●●●●●●●●●●●●●● ● ● ●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●● ●●●●●●● ●●●●●●●●●● ● ● 20 ●●●●●● ● ●●●●●●●●●●● ●●●●●● ●●●●●●●●●●●●●●●●●● ● ●●●●● ●● ●●●● ● ● ●● ●● ●●●●●●●●●●●●●●●●●●●● ●●●●●●●● ●● ●●●●●●● ●●●●●●● ●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●● ●●● ●● ●●●●● ● ● ●● ● ● ● ●● ● ● ●●●●●●●●●●●●●●●●●●●●● ●● ●●● ●● ●● ●●●●●●●● ●●●● ●●●●●●● ● ● ●● ● ● ●●●●●● ● ● ● ● ● ●●●● ● ● ● ●●●●●●●●●●●●●●●●●●● ● ●●● ● ● ●●●●●●●●●● ● ● ● ● ●●●● ●●●●● ●●●●●●●●●●●●●●●●●●●●●● ● ●● ● ● ● ● ●●● ●●●●●●●● ● ●●●● ● ●●● ● ●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●● ● ●● ● ● ● ● ●●●●● ●● ●● ● ● 10 ●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●● ●●● ●●●●●●●●●●● ●●●● ● ●●● ●●●●●●●●● ●●●●● ●●●●● ●●●●●● ●●●● ●●●● ●●●●●● ●●●● ●●●●● ●●● ●●● ●● ●● ● ● ● ● ● ●●●●● ●●● ● ●●●●● ●● ● ● ●●●● ●●●●●●●●●●● ●●●●●●● ● ●●●●●●●●●● ●●●●●●●●●● ●●●● ●●● ●● ● ●●● ●●●●●●●●● ● ●●●●● ● ● ● ●●● ●●● ● ●●●●● ● ●●● ● ● ●●●●●●●●● ●●●●●●●●● ●●●●●●●● ● ●●●●● ●● ●● ●● ●●●● ●●●● ● ●● ●●● ● ● ●● ●● ●● ●●● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 x Friday, 26 February 2010
  • 10. 3pt driving layup hook ● ● ● ● 70 ● ● ● ● ● ● 60 ● 50 ● ● ● ● ● ● 40 ● ● ●●● ●● ● ● ● ●●●●●●●●●●●●●●● ●●●● ●●● ●●●●●●●●●●●●●●●● ● ●●●●●●●●●●●●●●●● ●●●●●●●●●●● ●● ●●●●●●●● ● 30 ●●● ●●●●● ●●●● ● ●● ●●●●●●● ● ● ● ●●●●●● ●●●●●● ●●●●● ●●● ●●● ●●●●●● ●●●●● ●●●●● ●●●●● ●●●● ●●●● ●●● ●●● ●● ●●●● ●●●● ●●●● ●●●● ●●● ●● ●●● ●● ●●● ●●● ●●● ●●● ●●●● ● ●●●● ●●● 20 ●●● ●●●● ● ●●● ●●● ●● ●● ●● ●● ●● ● ●● ●● ● ● ● ● ● ●● ●●● ●●●●●●● ●● ● ● ●● ● ●● ● ●●●● ● ●● ● ●●●●● ● ● ●● ● ●● ● ●● ●● ● ● ● ●● ● ● ●●●●●●● ● ● 10 ●● ●● ●● ● ● ●● ●● ●●● ● ● ●●●●●●●● ●●● ●●●●●● ●●●●●● ●● ●● ● ●● ● ● ●● ● ●●●● ●●● ●●● ●● ● ●●●● ●●● ● ● ●●● ● ●● ●● ● ● ● ● ●● ●● ●● ●● ●● ● ●● ● ● ●● ● ● ● ● ●●● ● ● ● ● ●● ●● ●● ● jump layup turnaround jump y 70 60 50 40 30 ● ● ● ● ●●●●●●●● ●●●● ● ●●●●●●●●●●● ● ●●●●●●●●●●●● ●●●●●●●●● ● ●●●●●●●● ● ●●● ● ●●●●●●●●●●●●●●● ●●●●●● ● ●● ● ●●●●●●●●●●●●●●●●● ● ● ●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●● ●●●●●●● ●●●●●●●●●● ● ● 20 ●●●●●● ● ●●●●●●●●●●● ●●●●●● ●●●●●●●●●●●●●●●●●● ● ●●●●● ●● ●●●● ● ● ●● ●● ●●●●●●●●●●●●●●●●●●●● ●●●●●●●● ●● ●●●●●●● ●●●●●●● ●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●● ●●● ●● ●●●●● ● ● ●● ● ● ● ●● ● ● ●●●●●●●●●●●●●●●●●●●●● ●● ●●● ●● ●● ●●●●●●●● ●●●● ●●●●●●● ● ● ●● ● ● ●●●●●● ● ● ● ● ● ●●●● ● ● ● ●●●●●●●●●●●●●●●●●●● ● ●●● ● ● ●●●●●●●●●● ● ● ● ● ●●●● ●●●●● ●●●●●●●●●●●●●●●●●●●●●● ● ●● ● ● ● ● ●●● ●●●●●●●● ● ●●●● ● ●●● ● ●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●● ● ●● ● ● ● ● ●●●●● ●● ●● ● ● 10 ●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●● ●●● ●●●●●●●●●●● ●●●● ● ●●● ●●●●●●●●● ●●●●● ●●●●● ●●●●●● ●●●● ●●●● ●●●●●● ●●●● ●●●●● ●●● ●●● ●● ●● ● ● ● ● ● ●●●●● ●●● ● ●●●●● ●● ● ● ●●●● ●●●●●●●●●●● ●●●●●●● ● ●●●●●●●●●● ●●●●●●●●●● ●●●● ●●● ●● ● ●●● ●●●●●●●●● ● ●●●●● ● ● ● ●●● ●●● ● ●●●●● ● ●●● ● ● ●●●●●●●●● ●●●●●●●●● ●●●●●●●● ● ●●●●● ●● ●● ●● ●●●● ●●●● ● ●● ●●● ● ● ●● ●● ●● ●●● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 x Friday, 26 February 2010
  • 11. Marginal distribution of y 140 120 100 80 ..count.. 60 40 20 0 5 10 15 20 25 30 y Friday, 26 February 2010
  • 12. Marginal distribution of x 80 60 ..count.. 40 20 0 10 20 30 40 x Friday, 26 February 2010
  • 13. Joint distribution of x and y 2114 jumps 30 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 25 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 20 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● y 15 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 10 20 30 40 x Friday, 26 February 2010