,Chapter 6
Joint pf/pdf
f(x,,,...,xn) f(x;k)f(x;k) ...f(xn;k)
= =
I,f(xi,b)
SAMPLEMEAN E(X) E(X) =
E(x) nE(x) nxtE(x) E(X)
=
= =
SAMPLEVARIANCEVar(X) iVar(X) =
var (5): E ivar (x) W
=
i Var(x):IvawIX)
· as he, Var (X) ↓
CENTRAL LIMIT THEOREM when a suff larges X = N(M, )
x: DISTRIBUTION X-xi M
X zi E+.. Z,
=
+
.
+
Ei
=
ECX) K =
Var(X) =
2K
if Xinxi
X. + X2+... Xm +
e
XY +12+...+km
N(0,1)
t DISTRIBUTION T- ti S
in
--
fattertail than N
as k ->
a, T N(0,1)
-
T
FR
=
X-xi
XExist:K1:ECT) VarIT)
=
ECT) 0
=
for > 1 Var(T) 2
=
fork > 2
"
2:VarI)
=
, FDISTRIBUTION FEE, e
F
=
v/p ~ wx
V/K v-x
k
E(F) =- for K >2
k-2
⑧
#x NFk,p
·
Trtk -> T2 vF,,k
Chapter 7
BIAS(8) E(P) =
-
6
MEAN. SQUARED ERROR
MSE(E) E( 18-62) Var(B)+ (Bias (E)/2
=
=
E(((8 E(8)) +E(E) 0174
=
- -
"
=E)Y E)) +
+
E(zo)((-0)I
=Var(8) + [Bias (E)] ECOY -ECE(EY) tant
=
E(E)-
E(8)
·
Small MSEV =
O
·
MSE(M) E;as
= n = 0, MSES0
MEAN ABSOLUTE
DEVIATION
MAD(4) E(10-01)
=
Joint pf/pdf
f(x,,,...,xn) f(x;k)f(x;k) ...f(xn;k)
= =
I,f(xi,b)
SAMPLEMEAN E(X) E(X) =
E(x) nE(x) nxtE(x) E(X)
=
= =
SAMPLEVARIANCEVar(X) iVar(X) =
var (5): E ivar (x) W
=
i Var(x):IvawIX)
· as he, Var (X) ↓
CENTRAL LIMIT THEOREM when a suff larges X = N(M, )
x: DISTRIBUTION X-xi M
X zi E+.. Z,
=
+
.
+
Ei
=
ECX) K =
Var(X) =
2K
if Xinxi
X. + X2+... Xm +
e
XY +12+...+km
N(0,1)
t DISTRIBUTION T- ti S
in
--
fattertail than N
as k ->
a, T N(0,1)
-
T
FR
=
X-xi
XExist:K1:ECT) VarIT)
=
ECT) 0
=
for > 1 Var(T) 2
=
fork > 2
"
2:VarI)
=
, FDISTRIBUTION FEE, e
F
=
v/p ~ wx
V/K v-x
k
E(F) =- for K >2
k-2
⑧
#x NFk,p
·
Trtk -> T2 vF,,k
Chapter 7
BIAS(8) E(P) =
-
6
MEAN. SQUARED ERROR
MSE(E) E( 18-62) Var(B)+ (Bias (E)/2
=
=
E(((8 E(8)) +E(E) 0174
=
- -
"
=E)Y E)) +
+
E(zo)((-0)I
=Var(8) + [Bias (E)] ECOY -ECE(EY) tant
=
E(E)-
E(8)
·
Small MSEV =
O
·
MSE(M) E;as
= n = 0, MSES0
MEAN ABSOLUTE
DEVIATION
MAD(4) E(10-01)
=
