Math1313-FinalExamFormulaSheet

Math1313-FinalExamFormulaSheet - P <...

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1 2 1 2 x x y y m = ) ( 1 1 x x m y y = b mx y + = F cx x C + = ) ( sx x R = ) ( ) ( ) ( ) ( x C x R x P = . 1 then 0 and If 1 = = = a c b d D A bc ad D d c b a A t I Pr = ) 1 ( rt P A + = m r i = mt n = n i P A ) 1 ( + = n i A P + = ) 1 ( + = i i R S n 1 ) 1 ( + = i i R P n ) 1 ( 1 1 ) 1 ( + = n i iS R n i Pi R + = ) 1 ( 1 c c c B A B A I U = ) ( c c c B A B A U I = ) ( ) ( ) ( ) ( ) ( B A n B n A n B A n I U + = 1 2 3 ... ) 2 ( ) 1 ( ! = n n n n 0! = 1 )! ( ! ) , ( r n n r n P = )! ( ! ! ) , ( r n r n r n C = ) ( ) ( ) ( ) ( F E P F P E P F E P I U + = ) ( 1 ) ( E P E P c = ) ( ) ( ) ( S n E n E P = ) ( ) ( ) | ( A P B A P A B P I = ) | ( ) ( ) ( A B P A P B A P = I ) ( ) ( ) ( B P A P B A P = I for A and B independent. ) | ( ) ( ... ) | ( ) ( ) | ( ) ( ) | ( 1 1 n n i i i A E P A P A E P A P A E P A P E A P + + = where n i 1 . n n p x p x p x X E + + + = ... ) ( 2 2 1 1 2 2 2 2 2 1 1 ) ( ... ) ( ) ( ) ( μ + + + = n n x p x p x p X Var ) ( X Var = σ ) ( ) ( c E P E P ) ( ) ( E P E P c b a a E P + = ) ( 2 1 1 ) ( k k X k P + x n x q p x n C x X P = = ) , ( ) ( 1 = + q p np = npq x Var = ) ( npq = [] ) ( 1 2 1 ) ( z Z z P z Z
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Unformatted text preview: P < < + = < > = > a Z P a X P ) ( < = < b Z P b X P ) ( < < = < < b Z a P b X a P ) (...
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