Chapter 9: Testing hypotheses
(For your reference ONLY, not for examination)
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Blo
Errata for Chapter 8:
Page 9, line -6: The estimate/estimator of
Page 12, line +3: Insert two , as The likelihood of , as a function of
x1 , . . . , xn , is dened as
d ()
= () =
Page 15, line -4:
d
d 2 ( )
2
Page 15, line -1: (2) () =
= nX < 0
d 2 =
Pag
Chapter 8: Estimation of Parameters and
Fitting of Probability Distribution
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Bloc
Errata for Chapter 6:
Page 6, line -6: X N (, 2 )
Page 6, line -5: [(X )/]2 2
1
Page 8, line -1: Var(T )
Page 10, line 5: X =
1
n
n
Xi
i =1
Page 13, line -2: Computation of
Page 14: Remove this page
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Dr. Man-Wai HO (stahm
Chapter 6: Distributions Derived from the
Normal Distribution
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Block S3)
Dr. Man-
Errata for Chapter 5:
n
Xi and
Page 4, line -1: happen to
i =1
1
n
n
Xi ?
i =1
Page 6, line -4:
an average of independent and identically distributed (iid) r.v.s
1
Page 8, line -3:
n
n
i =1
X i
Page 8, line -1:
1
The limiting behavior of
n
n
Xi when n
Chapter 5: Limit Theorems
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Block S3)
Dr. Man-Wai HO ([email protected])
ST5201(NU
Errata for Chapter 4:
Page 7, line +2: an informative number
Page 10, line +4: Replace (n y )! by (n 1 y )!
Page 15, line +4,+5: Replace p (x ) by pX (x )
Page 15, line +6,+7: Replace f (x ) by fX (x )
Page 21, line +2: Expectation of A Special Function o
Chapter 4: Expected Values
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Block S3)
Dr. Man-Wai HO ([email protected])
ST5201(N
Example: Expectation of a t Distribution
Z
Dene the t distribution with n degrees of freedom by T =
where
X /n
Z N (0, 1) and X 2 , for n = 1, 2, . . ., are independent. The expected
n
value of T can be obtained by
1
1
nE Z
= nE (Z )E = 0
X
X
1, as E (Z
Errata for Chapter 3:
Page 5, line -1: Add the following
For diversication: How do X1 , . . . , XN vary simultaneously?
Page 17, line -4: Add behind the equation
f (x , y ) dx dy
=
A
Page 22, line +2: Clearly, f (x , y ) 0 for < x , y < .
Page 22, line -2
Chapter 3: Joint Distributions
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Block S3)
Dr. Man-Wai HO ([email protected])
ST52
Chapter 2: Random Variables
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Block S3)
Dr. Man-Wai HO ([email protected])
ST5201(
Supplementary Pages I
An illustration of point 1 at Page 39:
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ST5201(NUS) Ch.1
66 / 69
Supplementary Pages II
An illustration of point 2 at Page 39:
Substituting a = b = 1 in the expansion
Chapter 1: Probability
ST5201 Basic Statistical Theory1
(Academic Year 2012/13)
Department of Statistics & Applied Probability (DSAP); National University of Singapore (NUS)1
Tuesday, 7-10pm (LT20, Block S3)
Dr. Man-Wai HO ([email protected])
ST5201(NUS)