Basic Math Tools
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Appendix A
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The Summation Operator
1 2 3
1
......n
i n
i
x x x x x
1 1
.2 :n n
i i
i i
PS cx c x
1
.1:n
i
PS c nc
1 1 1
.3 : ( )n n n
i i i i
i i i
PS ax by a x b y
1 1 1
: / ( ) / ( )n n n
i i i i
i i i
Common error x y x y
_
1
: (1 / )n
i
i
Average x n x
2_ _ _
2( ) 0 ( )n n n
i i ix x but x x x n x
_ _ _ _ _ _n n n n
x x x x x x n x 1 1 1 1i i i i
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Linear Functions
1 x
1 1 /y x or y x
0 1 1 2 2(2) y x x
0 1 1 2 2y x x
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0 1 1 2 2y x x
*
1 2int : / ( 2 )Turning Po x
1 2
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Wa e Function
. . exp . expwage er er
exp .48 [2 .008 ] 30er
First year of experience is worth .48 y=.48 exper -2(.008)exper
with exper=1 and
ex er=0
Tenth year of experience is worth .32 . - .
exper=10
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Natural Logarithm
log(x)
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We are often interested in %Y/%X
It turns out that lo Y / lo x is a ver oodapproximation
Also Log(x1)-Log(X0) is a very goodapproximation for % x
Many random variables arent normally,
