MAT221Formulas-2008Fall - Formulas for MAT 221 Chapter 1 :...

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F o r m u l a s f o r M A T 2 2 1 C h a p t e r 1 : L o o k i n g a t D a t a - D i s t r i b u t i o n s S t a n d a r d d e v i a t i o n : s = z - s c o r e : z = ! - J ! P r o b a b i l i t y d i s i r i b u t i o n ( i ) M e a n : í . y : o t p l * t 2 7 t 2 ¡ , . , + : r : k ] ) k - - D r , p , . ( i ì ) V a r i a n c e : o 2 , = ( r 1 - þ . v ) 2 h I ( r 2 - p . x ) 2 p 2 + ( i i i ) I f a a n d L , a r e f i x e d n u m b e r s , t h e n t ( r ¡ - p y ) 2 p ¡ : Ð ( : r ¿ * p x ) 2 p ¡ / t I - , , . / r , - / ; + I r . , , - , t ' ? - / ; ì r I . t l - n i z l C h a p t e r 2 : L o o k i n g a t D a t a - R e l a t i o n s h i p s 5 " = " * r ( * - ) ( 1 7 ) - " = ( " + ) I " * 3 2 6 . L e a s t - s q u a r e s r e g r e s s i o n l i n e : g : a * å 2 , w h e r e ò = r a n d a : E - b r . C h a p t e r 4 : P r o b a b i l i t y : T h e S t u d y o f R a n d o m n e s s 7 . P r o b a b i l i t y R u l e s ( ù P ( A " ) : 1 - P ( A ) ( i i ) I f e v e n i s A a n d B a r e d i s j o i n t , P ( A o r B ) : P ( A ) + p ( B ) . ( i i i ) F o r a n y e v e n t s A a n d B , P ( , 4 o t B ) = P ( A ) + p ( B ) - I r ( A a n ð , I J ) . ( i v ) I l e v e n t s A a n d B a r e i n d e p e n d e n r , P ( A a n d n ) = p ( Ð p @ ) . ( v ) F o r a n y c v e n t s A a n d B , I , ( , 4 a n d t s ) = p ( A ) . I ' ( R A ) . ( v i ) W h e n P ( , 4 ) > 0 , P ( l l t A ) = " , o ? l l ' , ( v i i ) B a y e s ' s R u l e : S u p p o s e t h a t f u , A 2 , . . . , A k ¿ r r e d i s j o i n t e v c n t s w h o s e p r o b a b i l i t j c s a r e n o t 0 a n d a d d t o e x a c t l ) , 1 , I f C i s a n ) ¡ o t h e r e v c n t w h o s e p r o b a b i l i t y i s n o t 0 o ¡ 1 , P ( A r l C \ = P ( C l A . t ) P ( A , ) P ( C 1 . 4 1 ) P ( A t ) 1 P ( C l A 2 ) p ( A 2 ) + , , + p ( C l A k ) p ( A h ) t t a . t . t , x - a 1 - b ¡ t . y , o f ; . , , . , . = ¡ | 6 2 ,
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I f X a n d Y a r c r ¿ u r d o m v a r i a b l e s a n d i f X a n d l ' ¿ ¡ e i n d e p c n d e n t , t h e n ¡ r ¡ 1 y = l 1 . \ + / i ) . t h c n 0 . \ + ) , ( / . Y - 1 - t / ) o ? x - v = o 2 Y + t T C h a p t e r 5 : F l o m P r o b a b i l i t y t o I n f e r e n c e 9 . R i n o m i a l d i s t l i b u t i o n : X - B ( n , p ) ( i ) B i n o m i a l c o e f f i c i e n t : ( i ) : E n # T n , w h e r c n ! = n x ( n - l ) x ( n - 2 ) x . . x 3 x 2 x 1 . ( i i ) B i n o m i a l p r o b a b i l i t y : P ( X : k ) : ( i ) p r ( t - p ) ( n - h ) f o r k : 0 , 1 , . . . , ¡ ¿ ( ü i ) t r x = n p ( i v ) o ¡ - J n e l : Ã ( v ) F o r t h e s a m p ì e p r o p o r t i o n , p , þ p = p , " þ : { + 1 0 . L e t t b e t h e m e a n o f a n S R S o f s i z e n f r o m a p o p u l a t i o n h a v i n g m c a n ¡ r a u d s t a n d a r d d e v i a t i o n o T h e n t l ¡ = t t , o , = o l t / î C h a p t e r 6 : I n t r o d u c t i o n t o I n f e r e n c e
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MAT221Formulas-2008Fall - Formulas for MAT 221 Chapter 1 :...

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