Stat 5101 (Geyer) Fall 2011
Homework Assignment 1
Due Wednesday, September 14, 2011
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
Stat 5101 (Geyer) Fall 2011
Homework Assignment 2
Due Wednesday, September 21, 2011
Solve each problem. Explain your reasoning. No credit for answers with
no explanation.
2-1. Suppose we have a PMF fX with domain S (the original sample
space), and we have
Stat 5101 (Geyer) Fall 2011
Homework Assignment 10
Due Wednesday, November 30, 2011
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
Stat 5101 (Geyer) Fall 2011
Homework Assignment 12
Due Wednesday, December 14, 2011
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
Stat 5101 (Geyer) Fall 2011
Homework Assignment 11
Due Wednesday, December 7, 2011
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
Stat 5101 (Geyer) Fall 2011
Homework Assignment 9
Due Wednesday, November 23, 2011
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
Stat 5101 (Geyer) Fall 2011
Homework Assignment 8
Due Wednesday, November 9, 2011
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 2011
Homework Assignment 7
Due Wednesday, November 2, 2011
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 2011
Homework Assignment 6
Due Wednesday, October 26, 2011
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 2011
Homework Assignment 5
Due Wednesday, October 19, 2011
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 2011
Homework Assignment 4
Due Wednesday, October 5, 2011
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 5101 (Geyer) Fall 2011
Homework Assignment 3
Due Wednesday, September 28, 2011
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
Stat 5101 Lecture Slides
Deck 7
Charles J. Geyer
School of Statistics
University of Minnesota
1
Asymptotic Approximation
The last big subject in probability theory is asymptotic approximation, also called asymptotics, also called large sample theory.
We h
Stat 5101 Lecture Slides
Deck 5
Charles J. Geyer
School of Statistics
University of Minnesota
1
Joint and Marginal Distributions
When we have two random variables X and Y under discussion,
a useful shorthand calls the distribution of the random vector
(X,
Stat 5101 Lecture Slides
Deck 4
Charles J. Geyer
School of Statistics
University of Minnesota
1
Quantiles
If X is a random variable and 0 < q < 1, then the q -th quantile
of X (or of the distribution of X ) is any number x such that
Pr(X x) q
and
Pr(X x)
Stat 5101 Lecture Slides
Deck 6
Charles J. Geyer
School of Statistics
University of Minnesota
1
Existence of Integrals
Just from the denition of integral as area under the curve, the
integral
b
g (x) dx
a
always exists when a and b are nite and g is bound
Stat 5101 Lecture Slides
Deck 3
Charles J. Geyer
School of Statistics
University of Minnesota
1
Deja Vu
Now we go back to the beginning and do everything again.
2
Probability Mass Functions
A probability mass function (PMF) is a function
f
S R
whose domai
Stat 5101 Lecture Slides
Deck 2
Charles J. Geyer
School of Statistics
University of Minnesota
1
Axioms
An expectation operator is a mapping X E (X ) of random
variables to real numbers that satises the following axioms:
E (X + Y ) = E (X ) + E (Y )
for an
Stat 5101 Lecture Slides
Deck 1
Charles J. Geyer
School of Statistics
University of Minnesota
1
Sets
In mathematics, a set is a collection of objects thought of as
one thing.
The objects in the set are called its elements.
The notation x S says that x is