Formulas

X =ni=1Xin

e S2 =ni=1(Xi X)2n 1 =

ni=1X

2i nX2

n 1

X =ki=1 fiXin

S2 =ki=1 fi(Xi X)2

n 1 e S =S2

Se X B(n, p), P (X = x) =(n

x

)px(1 p)nx, x = 0, 1, 2 . . . , n

Se X P (), P (X = x) = ex

x!, x = 0, 1, 2, . . .

Se X Geom(p) P (X = x) = p(1 p)x1, x = 1, 2, . . .

Se X Hipergeom(m,n, r) P (X = x) =(mx

)(nmrx

)(nr

) , x = 0, 1, . . . ,min(r,m).Se X B(n, p) e n (np 15 e n(1 p) 15), Xnp

np(1p) N(0, 1).

Se X Exp(), f(x) = ex, x > 0

(u) = 0

tu1etdt, u > 0

X N(, 2) e X

N(0, 1)

X N(, 2/n) e X /n N(0, 1)

X S/n t(n1) e (n 1)S

2

2 2(n1)

p pp(1p)n

N(0, 1)

X Y (1 2)S2c (1/n1 + 1/n2)

t(n1+n22) S2c =(n1 1)S2x + (n2 1)S2y

(n1 + n2 2)

1

D DS2D/n

t(n1) S2D =(n 1)n

i=1

(Di D)2

Intervalos de Confianca:

X z/2 n e X t/2 Sn p z/2

p(1p)n e p z/2

14n

1 =

ni=1

XiYi nXYni=1

X2i nX2, 0 = Y 1X,

= r =

ni=1

(Xi X)(Yi Y ) ni=1

(Xi X)2ni=1

(Yi Y )22Y/X =

ni=1

(Yi Yi)2

n 2

SQTotal =ni=1

(Yi Y )2 SQReg =ni=1

(Yi Y )2 SQErro =ni=1

(Yi Yi)2

R2 = SQRegSQTotal

SQTotal =ki=1

nij=1

(Yij Y)2 SQTrat =ki=1

ni(Yi Y)2

SQErro =ki=1

nij=1

(Yij Yi)2 F = QMTratQMErro

F[(k1);

(ki=1

nik)]

Intervalos de Confianca simultaneos:

(Yi Yi) t/(2m)QMErro

(1ni

+ 1ni)

2