FormulaSheetFinal_F09

# FormulaSheetFinal_F09 - ± n s t X x 2 Two Sample t-test CI...

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( 29 2 1 1 x x n s i x - - = ( 29 ( 29 ( 29 ( 29 [ ] ( 29 ( 29 [ ] - - - = - - - = = y i n i x i s y y s x x n Y Y n X X n Y X XY n r 1 2 2 2 2 1 1 ( 29 ( 29 ( 29 = - - = x y s s r X X n Y X XY n b 2 2 1 ) ( X b Y b - = 0 Population mean and variance of discrete random variable formulas : i i X p x = μ i i X p x 2 2 ) ( σ - = Dispersion of linear combinations of random variables: 2 2 2 X bX a b = + Y X Y X Y X ρσ 2 2 2 2 + + = + Y X Y X Y X 2 2 2 2 - + = - For a “weighted average” where a+b = 1: Y X Y X bY aX b a b a ρ 2 2 2 2 2 2 + + = + If X 1 2 are uncorrelated (so ρ = 0), then variance of a portfolio of n investments denoted X 1 , X 2 , X 3 , …X n ; each with a 1/n share, is: ( 29 2 2 2 2 2 2 2 2 ) / 1 ( 2 ) / 1 ( 2 ) / 1 ( 1 ) / 1 ( ... ) / 1 ( ) / 1 ( ... 2 1 2 1 X X X X X n X n X n n n n n n n = + + + = + + + Bayes’ rule: ) ( ) | ( ) ( ) | ( ) ( ) | ( ) ( ) ( ) | ( ) ( ) ( ) | ( C C A P A B P A P A B P A P A B P B P A P A B P B P B A P B A P + = = = For X with Binomial distribution: μ = np ; σ 2 = np(1-p) and the probability that X=k is k n k p p k n - - ) 1 (

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CI, α significance level, variance known: ± n Z X x σ α * 2 / ; variance unknown:
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Unformatted text preview: ± n s t X x * 2 / Two Sample t-test CI, α significance level: 2 2 2 1 2 1 * 2 / 2 1 ) ( n s n s t x x + ±-; t-calculated: 2 2 2 1 2 1 2 1 ) ( n s n s x x t +-= Two Sample, Pooled t-test CI, α significance level: 2 1 * 2 / 2 1 1 1 ) ( n n s t x x p + ±-; t-calc. 2 1 2 1 1 1 ) ( n n s x x t p +-= pooled sample standard deviation = 2 ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1-+-+-= n n s n s n s p Standard Error of Regression: SE e = 2 2-= ∑ n e s i e ; t-calc. to test H : ρ = 0 is 2 1 2 r n r t--=...
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## This note was uploaded on 12/06/2009 for the course ECON 41 taught by Professor Guggenberger during the Spring '07 term at UCLA.

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FormulaSheetFinal_F09 - ± n s t X x 2 Two Sample t-test CI...

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