Probability Handouts
Probability Handouts
Preface
1
Randomness and Probability
2
Working with Probabilities
3
Interpreting Probabilities
4
Probability Models: Outcomes, Events, Random Variables, and Probability Measures
5
Introduction to Simulation
6
Conditioning
7
Marginal Distributions
8
Averages and Standard Deviation
9
Joint Distributions and Correlation
10
Conditional Distributions
11
Multiplication Rule and Law of Total Probability
12
Bayes Rule
13
Independence
14
Equally Likely Outcomes, Counting Rules, and Uniform Probability Meaures
15
Discrete Random Variables: Probability Mass Functions
16
Continuous Random Variables: Probability Density Functions
17
Cumulative Distribution Functions and Quantile Functions
18
Distributions of Transformations of Random Variables
19
Joint Distributions
20
Conditional Distributions
21
Expected Value
22
Variance and standard deviation
23
Covariance and Correlation
24
Expected Values of Linear Combinations of Random Variables
25
Conditional Expected Value
26
Binomial and Negative Binomial Distributions
27
Poisson Distributions
28
Exponential Distributions
29
Normal Distributions
30
Joint Normal Distributions
31
Central Limit Theorem
References
Appendices
Some Problem-Solving Strategies
Summary of Some Common Distributions
Probability Handouts
Author
Kevin Ross
Published
June 17, 2022
Preface
A selection of Handouts for STAT 305 and STAT 350.
1
Randomness and Probability