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# 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
1. #### A particular slide catching your eye?

Clipping is a handy way to collect important slides you want to go back to later.