Stat 5101 Lecture Slides: Deck 1
Probability and Expectation on Finite
Sample Spaces
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

Stat 5101 Lecture Slides: Deck 2
Axioms for Probability and Expectation,
Consequences of Linearity of Expectation,
Random Vectors, Time Series, Laws of
Large Numbers, Bernoulli, Binomial,
Hypergeometric, and Discrete Uniform
Distributions
Charles J. Geyer

Stat 5101 Lecture Slides: Deck 6
Existence of Integrals and Infinite Sums,
Countable Additivity and Monotone
Convergence, Existence of Moments,
Correlation
Charles J. Geyer
School of Statistics
University of Minnesota
1
Existence of Integrals
Just from th

Stat 5101 Lecture Slides: Deck 7
Asymptotics, also called Large Sample
Theory
Charles J. Geyer
School of Statistics
University of Minnesota
1
Asymptotic Approximation
The last big subject in probability theory is asymptotic approximation, also called asym

Stat 5101 Lecture Slides: Deck 5
Conditional Probability and Expectation,
Poisson Process, Multinomial and
Multivariate Normal Distributions
Charles J. Geyer
School of Statistics
University of Minnesota
1
Joint and Marginal Distributions
When we have two

Stat 5101 Lecture Slides: Deck 4
Quantiles and Best Prediction
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 suc

Stat 5101 Lecture Slides: Deck 2
Axioms for Probability and Expectation,
Consequences of Linearity of Expectation,
Random Vectors, Time Series, Laws of
Large Numbers, Bernoulli, Binomial,
Hypergeometric, and Discrete Uniform
Distributions
Charles J. Geyer

Stat 5101 Lecture Slides: Deck 3
Probability and Expectation on Infinite
Sample Spaces, Poisson, Geometric,
Negative Binomial, Continuous Uniform,
Exponential, Gamma, Beta, Normal, and
Chi-Square Distributions
Charles J. Geyer
School of Statistics
Univers

Stat 5101 Lecture Slides: Deck 1
Probability and Expectation on Finite
Sample Spaces
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