Formula Sheet

𝐸 𝑟! = ∑𝑝 𝑠 𝑟!(𝑠) 𝜎!! = ∑𝑝 𝑠 𝑟! 𝑠 − 𝐸 𝑟! !

𝜎!" = ∑𝑝 𝑠 𝑟! 𝑠 − 𝐸 𝑟! 𝑟! 𝑠 − 𝐸 𝑟! 𝜌!" =!!"!!!!

( ) 212P PU E r Aσ= − *

2

( )P f

P

E r ry

Aσ−

= ( )σ

−= P f

PP

E r rS

( ) ( ) (1 ) [ ( ) ]c p f f p fE r yE r y r r y E r r= + − = + − 𝜎! = 𝑦𝜎!

( ) ( ) ( )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 rσ σ σ= + +

2

1 1 1( ) ( ) ( , )

n n n

P i i P i j i ji i j

E r w E r σ ww cov r r= = =

= =∑ ∑∑

2( )M f ME r r Aσ− =

( ) ( )2

cov ,[ ]i M

i i f i M fM

r rE r r E r rβ β

σ⎡ ⎤= − = −⎣ ⎦

𝑟! = 𝐸 𝑟! + 𝛽!𝑚 + 𝑒! ( ) ( ) ( )i i i M iR t R t e tα β= + +

𝜎!! = 𝛽!!𝜎!! + 𝜎!(𝑒!) 𝑐𝑜𝑣 𝑟! , 𝑟! = 𝛽!𝛽!𝜎!!

𝑟! = 𝐸 𝑟! + 𝛽!!𝐹! + 𝛽!!𝐹! + 𝑒! 𝐸 𝑟! = 𝑟! + 𝛽!!𝜆! + 𝛽!!𝜆!