13 Bivariate

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13 Bivariate

  1. 1. Stat310 Bivariate distributions Hadley Wickham Friday, 26 February 2010
  2. 2. 1. Test 2. Example 3. CDF 4. Expectation 5. Conditional distributions 6. Correlation Friday, 26 February 2010
  3. 3. Test Friday, 26 February 2010
  4. 4. 15 10 n 5 C B A 0 10 15 20 25 30 35 40 Grade Friday, 26 February 2010
  5. 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. 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
  7. 7. Example Friday, 26 February 2010
  8. 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. 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. 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. 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. 12. Marginal distribution of x 80 60 ..count.. 40 20 0 10 20 30 40 x Friday, 26 February 2010
  13. 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

×