Stat 5101 (Geyer) Fall 2009
Homework Assignment 2 Solutions
2-1. Suppose we have a PMF fX with domain S (the original sample
space), and we have a map g : S T that induces a probability model with
PMF fY with domain T (the new sample space) given by the f
Stat 5101 (Geyer) Fall 2009 Homework Assignment 4 Due Wednesday, October 7, 2009
Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your fo
Stat 5102 (Geyer) Spring 2015
Homework Assignment 4 Solutions
4-1. Calculate the ARE of the sample mean X n versus the sample median
Xn as an estimator of the center of symmetry for
(a) The Laplace location-scale family having density given in the brand
n
Statistics 5101, Fall 2010: Homework Assignment 2
1. Suppose X is a random variable having the discrete uniform distribution on the sample space cfw_1, 2, 3, 4, 5, 6. (a) Determine Pr(X < 4). (b) Determine Pr(X 4). (c) Determine Pr(6 < X < 10). 2. Suppose
Stat 5102 (Geyer) 2003 Midterm 2
Problem 1
(a) The more on condence intervals handout gave three condence intervals for this situation. Equation (2.19) pn + c2 c 2n pn (1 pn ) c2 + 4n2 n c2 1+ n pn (1 pn ) n
equation (2.20) pn c and equation (2.22) c g 1
Stat 5101 (Geyer) Fall 2009
Homework Assignment 7 Solutions
7-1.
If X has the Gam(, ) distribution, we calculated in class that
( + )
.
()
E (X ) =
(a) Find E (X 2 )
(b) Find var(X ).
None of your answers should contain gamma functions (use the gamma
func
Stat 5101 Final Exam (with Solutions)
Name
December 16, 2014
Student ID
1
The exam is closed book and closed notes. You may use three 8 2 11
sheets of paper with formulas, etc. You may use the handout on brand name
distributions. You may use a calculator.
Stat 5102 (Geyer) Final Exam
Problem 1
Looking at the simplest moment rst, E(Xi ) = = = 1,
we see that it is not a function of the unknown parameter and hence useless for nding a method of moments estimator. Moving up to the second central moment, 1 var(
Statistics 101 Homework 2
Solution
Assignment:
1. Do the following problems from the text, Intro Stats, 3rd Edition. If you have an earlier edition of the text, check with someone who has the 3rd Edition to make sure you do the correct problems. a) Chapte
Stat 5101 (Geyer) Fall 2014
Homework Assignment 5
Due Wednesday, October 15, 2014
Solve each problem. Explain your reasoning. No credit for answers with
no explanation. If the problem is a proof, then you need words as well as
formulas. Explain why your f
Stat 5101 (Geyer) Fall 2012
Homework Assignment 1 Solutions
1-1. For each of the following functions h either determine a constant c
such that c h that is, the function x c h(x) is a PMF or determine
that no such constant exists.
(a) the identity function
Stat 5101 (Geyer) Fall 2014
Homework Assignment 5 Solutions
5-1. Suppose X1 , X2 , . . . are IID random variables having mean and
variance 2 . For each i 1 dene
5
Yi =
Xi+j
j=1
Then Y1 , Y2 , . . . is called a moving average of order 5 time series, MA(5)
Stat 5101 Final Exam
December 17, 2008
Name
Student ID
1 The exam is closed book and closed notes. You may use three 8 2 11 sheets of paper with formulas, etc. You may also use the handouts on brand name distributions and Greek letters. Put all of your wo
Stat 5101 (Geyer) Fall 2009
Homework Assignment 5 Solutions
5-1. Suppose X1 , X2 , . . . are IID random variables having mean and
variance 2 . For each i 1 dene
5
Yi =
Xi+j
j =1
Then Y1 , Y2 , . . . is called a moving average of order 5 time series, MA(5)
Stat 5101 005 Fall 2012
Homework Assignment 1
Due Wednesday, September 12, 2012
Solve each problem. Explain your reasoning. No credit for answers with
no explanation.
1-1. For each of the following functions h either determine a constant c
such that c h t
Stat 5101 Final Exam
December 22, 2011
Name
Student ID
1 The exam is closed book and closed notes. You may use three 8 2 11 sheets of paper with formulas, etc. You may also use the handouts on "brand name distributions" and Greek letters. Put all of your
Stat 5101 Final Exam
December 18, 2009
Name
Student ID
1
The exam is closed book and closed notes. You may use three 8 2 11
sheets of paper with formulas, etc. You may also use the handouts on brand
name distributions and Greek letters. Put all of your wo
Stat 5101 (Geyer) Spring 2016
Homework Assignment 1
Due Wednesday, January 27, 2016
Solve each problem. Explain your reasoning. No credit for answers with
no explanation.
1-1. For each of the following functions h either determine a constant c
such that c
Up: Stat 5132
Midterm 2
Problem 1
(a)
This is a special case of homework problem 8-4 in the notes. The problem statement says that
where
. (Here
and s are fixed numbers calculated from the data, and given the data.)
denotes a random
variable with the post
Statistics 101 Homework 2
Due Friday, January 29, 2010
Homework is due on the due date at the end of the lecture. Reading: Assignment:
1. Do the following problems from the text, Intro Stats, 3rd Edition. If you have an earlier edition of the text, check
Stat 5101 (Geyer) Fall 2009
Homework Assignment 3 Solutions
3-1. Suppose that f is a PMF on a sample space S , suppose X and Y are
random variables in this probability model. Prove the following statements.
(a) E (X + Y ) = E (X ) + E (Y ).
(b) If X (s) 0
Stat 5101 (Geyer) Fall 2009
Homework Assignment 12 Solutions
12-1. Give the details of the argument that the Poi() distribution is approximately normal when is large.
Solution. This is like the argument for the binomial and gamma distributions (slides 363
Up: Stat 5132
Final
Problem 1
The test statistic is
Under the null hypothesis Z is standard normal. From Table I in Lindgren, the one-tailed P-value is 0.0537.
Problem 2
Welch's procedure uses the test statistic
Under the null hypothesis T has an approxim
Stat 5101 (Geyer) Fall 2012
Homework Assignment 8 Solutions
8-1. Let X have the standard Cauchy distribution, which has PDF dened
in the brand name distributions handout
f (x) =
1
1
,
1 + x2
< x < .
(a) Find the quantile function for X.
(b) Find the med
Stat 5101 (Geyer) Fall 2012
Homework Assignment 11 Solutions
11-1.
Suppose the random vector (X, Y ) has variance matrix
4 3
3 9
Find sd(X), sd(Y ), and cor(X, Y ). Note: cor(X, Y ) is correlation not covariance.
Solution.
cor(X, Y ) =
cov(X, Y )
3
1
=
=
Stat 5101 (Geyer) Fall 2009
Homework Assignment 8 Solutions
8-1. Let X have the standard Cauchy distribution, which has PDF dened
in the brand name distributions handout
f (x) =
1
1
,
1 + x2
< x < .
(a) Find the quantile function for X .
(b) Find the me
Generate a realization of U~unif(0,1) / Y~
unif(1,10) and create an object u / y to
store this realization with
u=runif(n=1) / y=runif(n=1, min=1, max=
10) / y=1+9*runif(n=1)
u/y
Generate a realization of Y1,.,Y100 that
are iid Unif(1,10) and create an ob
Statistics 101 Homework 8
Solution Assignment: 1. Do the following problems from the text, Intro Stats, 3rd Edition. If you have an earlier edition of the text, check with someone who has the 3rd Edition to make sure you do the correct problems. a) Chapte
Analysis of Time Series Data Using R1
ZONGWU CAIa,b,c
E-mail address:
a
[email protected]
Department of Mathematics & Statistics and Department of Economics,
University of North Carolina, Charlotte, NC 28223, U.S.A.
b
c
Wang Yanan Institute for Studies in Eco
STAT5102 Lecture Notes (1)
Samples
Statistic
Parameter
Likelihood and Log-likelihood
Sufficient Statistic
1
Samples: We start with the univariate data.
In this class samples are the realization of n independent and identically distributed (iid) rando
STAT5102 Lecture Notes (8)
We will study
Connection between T and Normal
How to use t-distribution to construct some
exact confidence intervals in Normal models
Probability properties of the t-distribution
1
Generate a T-distributed Random
Variable
Sup
STAT5102 Lecture Notes (7)
Plug-in Method
Confidence Intervals
1
Plug-in Method
We have seen that central limit theorem and
the asymptotic normality of MLEs can greatly
help us do statistical inference. However, there
is one more issue remained untouche