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BU205+-+Class+04+(Pre-Class+Slides).pdf

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▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯ Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ – ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. 1 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ – ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ – ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯ – ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯ – ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ – ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯ – ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯ Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. 2 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ Distribution of Daily P ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ Crises r 0.5 NCrisesof Probability o 0.4 b 0.3 0 0.37 b 0 ≤ P(x) ≤1 for all x 1 0.31 i 0.2 2 0.18 l 0.1 3 0.09 i 0 ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 4 0.04 y 0 1 2 3 4 5 5 0.01 Number of Crises ∑ P(x) =1 over all x Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ µ=E x =( ) ∑ x⋅P x)( x P(x) x P(x) x P(x) x P(x) xP⋅() -1 .1 -1 -.1 -1 .1 ▯▯ ▯▯ ▯▯▯ 0 .2 0 .3 0 .3 1 .4 1 .4 1 .4 ▯ ▯▯ ▯▯ 2 .2 2 .3 2 .3 ▯ ▯▯ ▯▯ ▯ ▯▯ ▯▯ 3 .1 3 .1 3 .1 1.0 1.0 1.2 ▯ ▯▯ ▯▯ ▯▯▯ DISTRIBUTIONES NO NO u = 2.1 Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. 3 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 2 2 2 σ = ∑ (x−µ ) ⋅ x)( σ = σ µ=E (x )= ∑ x⋅P x)(= .1 15 x P(x) ( x − µ ) 2 (x−µ ) 2⋅ xP)( x − µ ) x (x P x P(x) -1 .1 -2.2 4.84 .484 r 0.5 0 .2 -1.2 1.44 .288 0 70 3.0 . o 1 13 3.1 . b 0.4 1 .3 -0.2 0.04 .012 a 0.3 2 .2 0.8 0.64 .128 6 83 1.2 . b 0.2 7 92 0.3 . i 3 .2 1.8 3.24 .648 i 0.1 1.56 6 41 0.4 . t 0 5 10 0.5 . y 0 1 2 3 4 5 2 2 Number of Crises u = 2.1 σ =1.56 σ = σ = 1.56 ≅1.249 1.15 Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯ ▯▯▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯ ▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯ ▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 2 2 σ = ∑ ( x−µ ) ⋅ x)(=1.41 ▯ ▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 2 ▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ σ = σ = 1.41 = 1.19 Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. 4 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯ n! X Xn − ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ P(X) = pq⋅ ≤ for 0 Xn ▯▯▯▯▯▯▯▯ Xn! !X− ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯ ▯ • ▯▯▯▯▯ µ = n⋅ p ▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯ 2 = np⋅⋅q ▯▯▯▯▯▯▯▯▯ σ 2 ▯▯▯▯▯▯▯▯▯ σ = = σ np⋅⋅q Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ • ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ •▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ •▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ Family Children in Number of Listing of Sample Space ▯▯▯▯▯▯ ▯▯▯▯ ▯ Household Automobiles ▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ (A,B), (A,C), (A,D), (A,A), •▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ A Yes 3 (B,A), (B,B), (B,C), (B,D), B Yes 2 (C,A), (C,B), (C,C), (C,D), ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ C No 1 (D,A), (D,B), (D,C), (D,D) ▯▯▯▯▯▯ ▯▯▯▯ ▯ D Yes 2 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 J▯▯▯▯▯iley &▯▯▯▯s Canada▯ Ltd. 5 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ X P(X) • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯ 0 1/16 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 1 6/16 ▯▯▯▯▯▯▯▯▯▯▯▯ Possible 2 9/16 Sequences P(sequence) X 1 ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ (F,F) (.25)(.25) 0 n! x nx − ▯▯▯▯▯▯ ▯▯▯▯ ▯ P(X) = Xn! !X− pq ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ (S,F) (.75)(.25) 1 ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ 2! 0 02 − 1 ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ (F,S) (.25)(.75) 1 P(X) = 0 .7.5 25 = 0=.0625 ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ 0! 2 −0 ! 16 ▯▯▯▯▯▯ ▯▯▯▯ ▯ (S,S) (.75)(.75) 2 • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ !2 1 −12 6 ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ (XP )1== ( )− !21!1.25 = 0.375 = 16 ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯ ▯▯▯▯ ▯ • ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 2! 2 22 − 9 P(X) = 2 2!2 !2− .7.5 25 = 0=.5625 16 ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯ ▯▯▯▯ ▯ Business Statistics, Can. Ed. © 2010 John Wiley ▯▯▯▯▯s Canada▯▯▯▯d. ▯ Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ n! x−xn 2! 0 02 − ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ XP)(= pq P(X) = 0 .7.5 25 = 0.0625 !(nX−X ! 0! 2 −0 ! n! 2! 1 12 − P(X) =1= ..5 25 =0.375 1!2!− r!()r− 2! 2 22 − P(X) = 2 .7.5 25 = 0.5625 2!2!2− Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. 6 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ n = 20 ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ n! x−xn XP )(= ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ p = .06 pq !( n)−X ! ▯▯ ▯▯▯▯▯ q = .94 ▯ ▯▯▯▯▯ ▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ (XP≤ = ?) 2 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ !2 0 0 −20 0 (XP= )0= (.06 .94 = (1)(1)(.2901) = .2901 0!(20 − 0)! ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯ ▯▯▯▯ ▯▯▯▯▯ ▯▯▯ !2 0 1 −21 0 (XP )1== (.06 .94 = (20)(.06)(.3086) = .3703 1!(20 −1)! ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ 20! 2 02 2 − P(X) = = 2 ( .0.6 )( 94 ) ..=(()(.)1)0036 3283 2246 2!2( 2 − )! (XP≤ )2= (XP= )0+ (XP= )1+ (XP= )2 = .2901 +.3703 +.2246 = .8850 Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ n = 20 n = 20 PROBABILITY n = 20 PROBABILITY X 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 p = 0.40 X123.4.0.0.00 0 102.2 001.2 000.1 000.0 0 0.122 0.012 0.0010.000 0.000 0.000.000 0.0000.000 1 0.270 0.058 0.0070.000 0.000 0.000.000 0.0000.000 (XP= = ?)1 0 1 207.0 005.8 000.7 000.0 2 0.285 0.137 0.0280.003 0.000 0.000.000 0.0000.000 2 208.5 103.7 002.8 000.3 3 0.190 0.205 0.0720.012 0.001 0.000.000 0.0000.000 3 109.0 200.5 007.2 001.2 4 0.090 0.218 0.1300.035 0.005 0.000.000 0.0000.000 4 009.0 201.8 103.0 003.5 5 0.032 0.175 0.1790.075 0.015 0.000.000 0.0000.000 n! x−xn 5 003.2 107.5 107.9 007.5 6 0.009 0.109 0.1920.124 0.037 0.000.000 0.0000.000 XP)(= 6 000.9 100.9 109.2 102.4 7 0.002 0.055 0.1640.166 0.074 0.010.001 0.0000.000 pq 7 000.2 005.5 106.4 106.6 !(nX−X ! 8 0.000 0.022 0.1140.180 0.120 0.030.004 0.0000.000 8 000.0 002.2 101.4 108.0 9 0.000 0.007 0.0650.160 0.160 0.070.012 0.0000.000 9 000.0 000.7 006.5 106.0 10 0.000 0.002 0.0310.1170.176 0.1170.031 0.0020.000 10 10 10 0.0000.002 0.0310.117 11 0.000 0.000 0.0120.071 0.160 0.160.065 0.0070.000 11 0.000 0.0000.012 0.071 12 0.000 0.000 0.0040.035 0.120 0.180.114 0.0220.000 (XP= )1= 200C 10(.40 .60 12 0.0000.000 0.0040.035 13 0.000 0.000 0.0010.015 0.074 0.160.164 0.0550.002 13 0.0000.000 0.0010.015 14 0.000 0.000 0.0000.005 0.037 0.120.192 0.1090.009 14 0.0000.000 0.0000.005 =0.1171 15 0.000 0.000 0.0000.001 0.015 0.070.179 0.1750.032 15 0.0000.000 0.0000.001 16 0.000 0.000 0.0000.000 0.005 0.030.130 0.2180.090 16 0.0000.000 0.0000.000 17 0.000 0.000 0.0000.000 0.001 0.010.072 0.2050.190 17 0.0000.000 0.0000.000 18 0.000 0.000 0.0000.000 0.000 0.000.028 0.1370.285 18 0.0000.000 0.0000.000 19 0.000 0.000 0.0000.000 0.000 0.000.007 0.0580.270 19 0.0000.000 0.0000.000 20 0.000 0.000 0.0000.000 0.000 0.000.001 0.0120.122 20 0.0000.000 0.0000.000 Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. Business Statistics, Can. Ed. © 2010 John Wiley & Sons Canada, Ltd. 7 ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ ▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯▯ n = 20 n = 20 PROBABILITY n = 20 p =.06 50X.0 0.06 0.07 p = .06 003.585 0.2901 0.2342 q =.94
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