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Formula Sheet
๐ธ ๐! = โ๐ ๐ ๐!(๐ ) ๐!! = โ๐ ๐ ๐! ๐ โ ๐ธ ๐! !
๐!" = โ๐ ๐ ๐! ๐ โ ๐ธ ๐! ๐! ๐ โ ๐ธ ๐! ๐!" =!!"!!!!
( ) 212P PU E r Aฯ= โ *
2
( )P f
P
E r ry
Aฯโ
= ( )ฯ
โ= P f
PP
E r rS
( ) ( ) (1 ) [ ( ) ]c p f f p fE r yE r y r r y E r r= + โ = + โ ๐! = ๐ฆ๐!
( ) ( ) ( )P D D E EE r w E r w E r= + 2 2 2 2 2 2 ( , )P D D E E D E D Ew w w w cov r rฯ ฯ ฯ= + +
2
1 1 1( ) ( ) ( , )
n n n
P i i P i j i ji i j
E r w E r ฯ ww cov r r= = =
= =โ โโ
2( )M f ME r r Aฯโ =
( ) ( )2
cov ,[ ]i M
i i f i M fM
r rE r r E r rฮฒ ฮฒ
ฯโก โค= โ = โโฃ โฆ
๐! = ๐ธ ๐! + ๐ฝ!๐ + ๐! ( ) ( ) ( )i i i M iR t R t e tฮฑ ฮฒ= + +
๐!! = ๐ฝ!!๐!! + ๐!(๐!) ๐๐๐ฃ ๐! , ๐! = ๐ฝ!๐ฝ!๐!!
๐! = ๐ธ ๐! + ๐ฝ!!๐น! + ๐ฝ!!๐น! + ๐! ๐ธ ๐! = ๐! + ๐ฝ!!๐! + ๐ฝ!!๐!