Introduction to Probability
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Expected Values
Introduction to Probability
Vladimir Dobrushkin
http://www.cfm.brown.edu/people/dobrush/
Basics
Introduction
Review of Set Theory
Permutations
Combinations
Shuffling
PIE
Problems
Probability
Introduction
Sample Space
Events
Basic Relationships of Probability
Expected Values
Variance and Moments
Independence
Conditional Probabilities
Bayes' Theorem
Theorem of Total probability
Gambler's ruin problem
Problems
Random Variables
Basic Concepts
Distribution functions
Discrete distributions
Continuous distributions
Expected values
Median
Variance
Moments
Functions of a RV
More About Discrete Random Variables
Problems
Multivariable Distributions
Basic Concepts
Bivariate distributions
Marginal distributions
Conditional distributions
Dependent Random Variables
Covariance
Multivariable distributions
Functions of random variables
Types of convergence
Borel--Kolmogorov paradox
Problems
Discrete Random Variables
Basic Concepts
Bernoulli RV
Binomial Distribution
Multinomial Distribution
Geometric Distribution
Negative Binomial
Hypergeometric Distribution
Poisson Distribution
More About Discrete Random Variables
Problems
Continuous Random Variables
Introduction
Uniform Distribution
Exponential Distribution
Normal Distribution
Gamma Distribution
Beta Distribution
Chi-Square Distribution
Special Distributions
Mixed Random Variables
Problems
Sampling Distributions
Introduction
Chi-Square distribution
Sample mean and variance
t
distribution
F
distribution
Chebyshev inequality
Central limit theorem
Limit laws
Probability Bounds
Problems
Statistical Inference I: Classical Methods
Introduction
Point Estimation
Interval Estimation (Confidence Intervals)
Hypothesis Testing
Linear Regression
Problems
Statistical Inference II: Bayesian Inference
Bayesian Inference
Problems
Intro to Random Processes
Basic Concepts
Processing of Random Signals
Problems
Some Important Random Processes
Poisson Processes
Discrete-Time Markov Chains
Continuous-Time Markov Chains
Brownian Motion (Wiener Process)
Problems
Intro to Simulation Using MATLAB
TBD
TBD
TBD
TBD
Intro to Simulation Using R
TBD
TBD
Glossary
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Reference
Free Materials
Books
GFDL License
Statistics
with R
with Excel
Expected Values
