LIR 832 FALL 2005 Formula sheet mid-term

LIR 832 FALL 2005 Formula sheet mid-term - Formula Sheet:...

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Page 1 of 8 1 1 1 .: POPULTATION MEAN m X j j m µ = = 2 1 2 1 2 2 1 2 . () POPULATION VARIANCE m X POPULATION STANDARD DEVIATION X m i i m i i m σµ σσ =− == = = 3 1 1 . SAMPLE MEAN xx n i i n = = 4 1 1 1 1 22 1 1 . tan : SAMPLE VARIANCE s n sample s dard deviation ss n i i n i i n = = = Formula Sheet: Mid-term Exam: LIR 832 Fall, 2005
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Page 2 of 8 5 1 1 .v a r , (,) ( ) ( ) if X and Y are random iables from a population then COV X Y X Y and COV X Y m ix i m iy XY =− = = µµ ρ σσ 6 1 1 1 a r , ( ) ( ) If x and y are random iables from a sample then COV x y s n xx yy and r COV x y ss xy i i n i xy == −− = =
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Page 3 of 8 8 22 1 . () * ( ) PROBABILITY WEIGHTEDVARIANCE xp x gx g g G σµ =− = 9 1 COVARIANCE FOR PROBABILITY DISTRIBUTIONS COV X Y x y p x y gg g g g G (,) ( ) ( )( , ) = µµ 7 1 . * ( ) , var PROBABILITY WEIGHTED MEANS Ex x px where g indexes groups not individuals x is a value taken on by the random iable in question p x is the probability of x occuring g G g g µ == =
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Page 4 of 8 11.
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LIR 832 FALL 2005 Formula sheet mid-term - Formula Sheet:...

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