Glossary

A comprehensive glossary of all terms defined in this textbook, organized alphabetically.

This glossary will be populated as chapters are completed.

Categorical variable — A variable that records group membership rather than a numerical quantity. May be nominal (no ordering) or ordinal (natural ordering). (Chapter 1)

Combination — An unordered selection of $r$ objects from $n$ distinct objects: $C(n,r) = \binom{n}{r} = \frac{n!}{r!(n-r)!}$. (Chapter 2)

Continuous random variable — A random variable that can take any value in some interval of real numbers. (Chapter 5)

Cumulative distribution function (CDF) — For a random variable $X$, the function $F(x) = P(X \leq x)$. (Chapters 4, 5)

Discrete random variable — A random variable that takes countable values (finite or countably infinite). (Chapter 4)

Event — A subset of the sample space; a collection of outcomes. (Chapter 2)

Expected value — The weighted average of a random variable’s values, weighted by their probabilities: $E(X) = \sum x \cdot p(x)$ (discrete) or $E(X) = \int x \cdot f(x) \, dx$ (continuous). (Chapters 4, 5)

Individual — One item examined in a statistical investigation. (Chapter 1)

Moment generating function (MGF) — The function $M(t) = E(e^{tX})$, which uniquely determines a distribution. (Chapters 4, 5)

Parameter — A numerical summary computed from the entire population. (Chapter 1)

Permutation — An ordered arrangement of $r$ objects from $n$ distinct objects: $_nP_r = \frac{n!}{(n-r)!}$. (Chapter 2)

Population — The complete collection of all individuals of interest. (Chapter 1)

Probability density function (PDF) — A function $f(x)$ such that $P(a \leq X \leq b) = \int_a^b f(x) \, dx$ for a continuous random variable. (Chapter 5)

Probability mass function (PMF) — A function $p(x) = P(X = x)$ for a discrete random variable. (Chapter 4)

Random variable — A function that assigns a numerical value to each outcome in a sample space. (Chapters 3, 4)

Sample — A subset of the population that is actually observed. (Chapter 1)

Sample mean — $\bar{y} = \frac{1}{n}\sum_{i=1}^n y_i$, the average of the observed data values. (Chapter 1)

Sample space — The set of all possible outcomes of an experiment, denoted $S$. (Chapter 2)

Sample standard deviation — $s = \sqrt{s^2}$, the square root of the sample variance. (Chapter 1)

Sample variance — $s^2 = \frac{1}{n-1}\sum_{i=1}^n (y_i - \bar{y})^2$, a measure of spread in the data. (Chapter 1)

Statistic — A numerical summary computed from a sample. (Chapter 1)

Variable — The characteristic measured or recorded about each individual. (Chapter 1)

Variance — A measure of spread: $V(X) = E[(X - \mu)^2] = E(X^2) - [E(X)]^2$. (Chapters 4, 5)