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Páginas: 4 (871 palabras)
Publicado: 7 de febrero de 2012
1 n 1i
n
( xi
1
x)2 cov( x, y ) 1 n 1i
n
Sample coefficient of variation: Sample coefficient ofcorrelation: Probability
cv
r
s Sample covariance: x cov( x, y ) s X sY
( xi
1
x )( y i
y)
P( A B) P( B) Bayes Law: If A1 , A2 ,, Ak are mutually exclusive and A1 A2 Ak is the wholesample space, then P( B Ai ) P( Ai ) P( Ai B) P( B A1 ) P( A1 ) P( B Ak ) P( Ak ) Random Variables
Conditional probability:
P( A B)
Expected Value: Covariance:
E( X )
all x
xp( x)
(x
XVariance:
)( y
Y
2
V (X )
all x
(x
X
) 2 p( x)
all x
Y
x 2 p ( x)
2
Cov( X , Y )
y x
) p ( x, y )
y x
x y p ( x, y )
Coefficient of correlation: Binomialdistribution: Poisson distribution:
Cov( X , Y )
X Y
P( X P( X
Exponential: density function Normal: density function
X
n! p x (1 p) n x , x x!(n x)! x e , x 0,1, x) x! f ( x) e x , x 0 x)f ( x) 1 2 e
1 x 2
2
0,1,, n
,
x
Sampling distributions Central Limit theorem: is distributed approximately standard normal for any population. to within W units:
n Size of a samplewhen the population standard deviation is known, to estimate
z n
For proportions:
ˆ p p
2
2
W
For two populations:
p (1 p ) n X1 X 2 (
2 1
is distributed approximately standardnormal
1 2 2
2
)
is distributed approximately standard normal
n1
n2
Conditions Normal population (or any population with n sufficiently large) with 2 known.
Confidence intervalH0
Test Statistic
Ha
0
Reject H 0 when
z0 z0
z0
z z
z
2
For
X z
2
:
0
z0
X n
0
0
n
0
For
X t S
2
:
0
t0
t0
t
t
n with n 1 degrees offreedom.
0
t0
X S n
0
0
Normal population with 2 unknown
(n 1) S
2 2 2
0
t0
2 0 2 0
2 0
t
2
2
2
2 0 2 0
2
For
2
:
(n 1) S
2 1 2 2
2
2
2 0...
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