MATH 697
Syllabus
General Information
Course Description
Grade Distribution
Target Syllabus
Overview and Descriptive Statistics (Weeks 1-4)
Probability (Weeks 1-4)
Discrete Random Variables and Probability Distributions (Weeks 1-4)
Continuous Random Variables and Probability Distributions (Weeks 5-8)
Joint Probability Distributions (Weeks 5-8)
Sampling Distributions and Limits (Weeks 5-8)
Statistical Inference (Weeks 9-12)
Likelihood Inference (Weeks 9-12)
Regression and Correlation (Weeks 9-12)
Prerequisites
Install R and RStudio
R Packages
Introduction to R
Background Reading
Slides
Assignments
Quiz
R Code
0.1
Central Limit Theorem in Action
0.2
IMPC Dataset
Distribution Tables
0.3
Standard Normal
0.4
t-Distribution
I Part I
1
Overview and Descriptive Statistics
1.1
Populations and Samples
1.1.1
Variable
1.1.2
Branches of Statistics
1.2
Pictorial and Tabular Methods in Descriptive Statistics
1.3
Measures of Location
1.4
Measures of Variability
2
Probability
Introduction
Probability: A Measure of Uncertainty
2.1
Sample Spaces and Events
2.1.1
Sample Spaces
2.1.2
Events
2.2
Axioms, Interpretations, and Properties of Probability
2.3
Counting Techniques
2.3.1
Permutations
2.3.2
Combinations
2.4
Conditional Probability
2.4.1
Law of Total Probability
2.4.2
Bayes’ Rule
2.5
Independence
3
Discrete Random Variables and Probability Distributions
Introduction
3.1
Random Variables
3.2
Probability Distributions for Discrete Random Variables
3.3
Expected Values of Discrete Random Variables
3.4
Moments and Moment Generating Functions
3.5
The Binomial Probability Distribution
3.6
The Poisson Probability Distribution
4
Continuous Variables and Probability Distributions
Introduction
R Tutorial
A
Vectorization, *apply and for loops
A.1
Vectorization
A.2
Family of
*apply
functions
A.2.1
Loops vs. Apply
A.2.2
Descriptive Statistics using
*apply
A.2.3
Creating new columns using
sapply
A.2.4
Applying functions to subsets using
tapply
A.2.5
Nested for loops using
mapply
A.3
Creating dynamic documents with
mapply
B
Appendix B
References
Published with bookdown
MATH 697
Chapter 4
Continuous Variables and Probability Distributions
Introduction