Probability & Statistics

Instructor. Motoya Machida, Tennessee Technological University. (E-mail: mmachida@tntech.edu)

Description of probability course topics. We begin with the basic concepts of probability, such as events, random variables, independence, and conditional probability. Having developed these concepts, the remainder of the course concentrates on the methods of calculation in probability and their applications through exercises. The topics treated here are divided into the five major parts:

probabilistic models;
random variables;
discrete distributions;
continuous distributions;
joint distributions.

When completed, these topics will unify the understanding of density and distribution functions of various kinds, calculation and interpretation of moments, and distributions related to normal distributions.

Lecture contents	lecture note	presentation	quiz/test solutions	r source
Probabilistic models	note01.pdf	slides01.pdf	quiz01-2025.pdf quiz02-2025.pdf	inspect.r
Random variables	note02.pdf	slides02.pdf	quiz03-2025.pdf quiz04-2025.pdf test01-2025.pdf
Discrete distributions	note03.pdf	slides03.pdf	quiz05-2025.pdf quiz06-2025.pdf
Continuous distributions	note04.pdf chisquare.pdf normal.pdf	slides04.pdf	quiz07-2025.pdf test02-2025.pdf	chisquare.r normal.r
Joint distributions	note05.pdf	slides05.pdf	quiz08-2026.pdf quiz09-2026.pdf

Description of statistics course topics. We continue topics of probability course, and integrate them with the treatise of mathematical statistics. We begin with further exploration of probability: (I) sampling distributions and (II) limiting distributions. Then we develop the core concepts of (III) statistical inference, covering the topics of theory of point estimation and hypothesis testing. The investigation of probability and statistics culminates in understanding of (IV) maximum-likelihood methods and their properties.

Lecture contents	lecture note	presentation	quiz/test solutions	r source
Sampling distributions	note06.pdf chisquare.pdf ttable.pdf ftable.pdf	slides06.pdf		tdemo.R fdemo.R
Limiting distributions	note07.pdf	slides07.pdf
Statistical inference
Maximum-likelihood methods

R code. R is free software/platform for statistical computing and graphics, and R code is made available for you to run it in your own machine. R can be installed on Windows, Linux, and Mac, and downloaded from CRAN R project. Each “command” is executed in an interactive manner, known as “interpretor,” and is requested in a form of “function.” For example,

> x <- c(3,1,2)

is the instruction to create an array x which contains the values of 3,1,2.

R source files. R functions are prepared as external source files (usually with extension ".r" or ".R"), and must be sourced in R in advance with the command

> source("[script filename]")

Or, call it by

> source(file.choose())

and choose a source file interactively.

Working directory. Your external source files must be found in the working directory and recognized by R. You can always change the working directory from R via [File]->[Change dir...]. Alternatively you can set the working directory by

> setwd("[pathname]")

R Studio. On top of R you may want to use R Studio. It is an integrated development environment (IDE) for R. Follow their instruction to download and install DESKTOP R STUDIO in your PC.