Probability distributions Carola Wenk 11/13/13 CMPS/MATH 2170 - PowerPoint PPT Presentation

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CMPS/MATH 2170 -- Fall 2013 Discrete Mathematics Probability distributions Carola Wenk 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 1 Rolling two dice Sum of two fair six-sided dice: S = {1,2,3,4,5,6} x {1,2,3,4,5,6} X((s 1 ,s

CMPS/MATH 2170 -- Fall 2013 Discrete Mathematics Probability distributions Carola Wenk 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 1
Rolling two dice Sum of two fair six-sided dice: S = {1,2,3,4,5,6} x {1,2,3,4,5,6} X((s 1 ,s 2 )) = s 1 +s 2 x P(X=x) {X=x} P(X=x) 2 1/36 {(1,1)} 0.18 3 2/36 {(1,2),(2,1)} 0.16 4 3/36 {(1,3),(2,2),(3,1)} 0.14 5 4/36 {(1,4),(2,3),(3,2),(4,1)} 0.12 6 5/36 {(1,5),(2,4),(3,3),(4,2),(5,1)} 0.10 7 6/36 {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} 0.08 0.06 8 5/36 {(2,6),(3,5),(4,4),(5,3),(6,2)} 0.04 9 4/36 {(3,6),(4,5),(5,4),(6,3)} 0.02 10 3/36 {(4,6),(5,5),(6,4)} 0.00 11 2/36 {(5,6),(6,5)} 1 2 3 4 5 6 7 8 9 10 11 12 1/36 {(6,6)} Probability function or probability distribution: p(x) = P(X=x) 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 2
Rolling two dice x 2 p(x) x p(x) x p(x) 2 1/36 2/36 4/36 3 2/36 6/36 18/36 4 3/36 12/36 48/36 5 4/36 20/36 100/36 6 5/36 30/36 180/36 P(X=x) 7 6/36 42/36 294/36 0.18 8 5/36 40/36 320/36 0.16 9 4/36 36/36 324/36 0.14 10 3/36 30/36 300/36 0.12 0.10 11 2/36 22/36 242/36 0.08 12 1/36 12/36 144/36 0.06 0.04 Sum 36/36 252/36 1974/36 0.02 = 1 = 7 = 54.833 0.00 1 2 3 4 5 6 7 8 9 10 11 Probability function or probability distribution: p(x) = P(X=x) 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 3
Binomial Distribution 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 4
Geometric Distribution 11/13/13 CMPS/MATH 2170 Discrete Mathematics -- Carola Wenk 5

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