By Klotz J.H.

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To illustrate these definitions, consider the sample space for the roll of two dice . The first die is red and the second die is green and each die has 1,2,3,4,5, 6 on the faces. Then if we use the notation (i, j) where i, j ∈ {1, 2, 3, 4, 5, 6} for an outcome with the first coordinate representing the up face for the red die and the second coordinate the up face for the green die, the sample space is S = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) } Let the event A be the 1st (red) die is 3 or less A = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)} 40 CHAPTER 2.

We say the events {A1 , A2 , . . , An } are mutually independent if we have jk jk P (Ai ) for j1 < j2 < . . < jk and all k = 2, 3, . . , n . Ai ) = P( i=j1 i=j1 It is possible to have pairwise independence but not mutual independence. As an example, consider the sample space for the roll of two dice with probability 1/36 for each outcome. Let the event A1 be first die odd, A2 be the second die odd, and A3 be the sum is odd. 5. PROBLEMS And we have pairwise independence. Since the sum of two odd numbers is even, P (A1 ∩ A2 ∩ A3 ) = 0 = 18 36 18 36 18 36 = P (A1)P (A2 )P (A3 ) and we do not have mutual independence.

9. Calculate the inter quartile range IQR. 10. Calculate the mean absolute deviation about the median D. M. and the R Development Core Team (2004). An Introduction to R. org 36 CHAPTER 1. DESCRIPTIVE STATISTICS 11. Calculate the sample variance S 2 . 12. 4). 13. 1. 4 4 6 10 12 5 14. Calculate the sample median. 15. Calculate the Walsh sum median. 16. Calculate the sample mean. 17. 13). 18. 4). 19. 13). 20. Prove D ≤ R/2. 1 The Sample Space Consider a random experiment which has a variety of possible outcomes.

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