Publications by Paul Regier
MATH 4883 - HW2
Random Variables A continuous random variable \(X\) takes a range of values, which may be finite or infinite in extent (e.g. \([0, 1]\), \([0, \infty)\), \((−\infty, \infty)\)), whereby the probability of \(X\) falling between two values a and b is: \[P(a<X<b)=\int_a^b f(x)dx\] For a special given function called a probability distribution fun...
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MRA - HW3
1 Central Limit Theorem Let \(X_1\), \(X_2\), …, \(X_n\) are \(n\) randomly sampled observations from a population with mean \(E(X_i)=\mu\) and variance \(Var(X_i)=\sigma^2\). Then the sample mean \(\bar{X}=\frac{\sum_i^n X_i}{n}\) can be approximated by a normal density function. Furthermore, \(E(\bar{X})=\mu\), and \(Var(\bar{X})=\frac{\sigm...
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MATH 4883 - HW5
1 Inference for Linear Regression Is this assignment we will develop the theory for making inferences about our regression model: \[y = \beta_0 + \beta_1x+\epsilon\] Where \(\beta_0\) and \(\beta_1\) are unknown parameters (corresponding to y-intercept and slope of linear model), and \(\epsilon\) is the random error. To test whether x makes any c...
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MRA HW6
1 Coefficient of Determination Recall the correlation \(R = \frac{SS_{xy}}{\sqrt{SS_{xx}SS_{yy}}}\). Show that \(R^2 = \frac{\sum_i^n (y_i-\bar{y})^2 - \sum_i^n (y_i-\hat{y_i})^2 }{\sum_i^n (y_i-\bar{y})^2 } = \frac{SS_{yy}-SSE}{SS_{yy}}\). \(R^2\) is called the the coefficient of determination or multiple R-squared. Practical interpretation of...
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BCSSI 2021 Probability Session Notes
1 Preliminaries Do the following (all free): Download and install R https://cran.r-project.org/ Download and install Desktop RStudio https://rstudio.com/products/rstudio/download/ (choose the free version) R is a free software environment for statistical computing and graphics. It compiles and runs on a wide variety of UNIX platforms, Windows, ...
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Elementary Statistics Syllabus
Instructor: Dr. Paul Regier Time: MWF 10:10am-11:10am Email: pregier@usao.edu Place: Austin Hall 108 Office hours: posted in Canvas 1 Course Description This course is an introduction to statistical principles and probability, with applications in business, social and behavioral sciences. (3 hours) Prerequisite: ACT mathematics score of 19 or...
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MMW Syllabus
Instructor: Dr. Paul Regier Time: Tues/Thurs, 1:30-2:55pm Email: pregier@usao.edu Place: On Zoom (see Canvas) Office hours: posted in Canvas 1 Course Description This course explores the structure, language, and thought processes of mathematics. 1.1 Learning Outcomes Upon completion of the course, students will be able to: Apply concepts fr...
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Document
Playing the lottery In a certain state’s lottery, \(64\) balls numbered 1 through \(64\) are placed in a machine and six of them are drawn at random. If the six numbers drawn match the numbers that a player had chosen, the player wins jackpot $1,000,000. If numbers drawn match any 5 of the numbers that a player had chosen, the player wins $1,00...
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Foundations of Math - Course Notes
These notes are derived from Richard Hammack’s textbook Book of Proof and course notes graciously given to me by Milos Savic. Much thanks to their creative, passionate work! Chapter 1 - Sets 1.1 Introduction to Sets What is a set? A set is a collection of things. What are the things? The things are called elements. What is an element? Ok, a...
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Calc IV - Syllabus
Instructor: Dr. Paul Regier Time: MWF 12:20 pm - 1:20 pm Email: pregier@usao.edu Place: Austin Hall 213 Office hours: posted in Canvas 1 Course Description This course covers the topics of vector calculus, multivariable functions, and their derivatives; extreme values; Lagrange multipliers; multiple integrals; integration in vector fields. (T...
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