Probability and Statistics – Introductory Lecture Vocabulary

Vocabulary flashcards covering key terms, statistical tests, and software tools introduced in the Probability and Statistics course outline.

Probability

A measure, between 0 and 1, that quantifies the likelihood of an event occurring.

Statistics

The science of collecting, analyzing, interpreting, and presenting data.

Event Probability

The probability assigned to a specific outcome or set of outcomes within a sample space.

Random Numbers

Numbers generated in such a way that each possible value has a fixed, known probability of occurrence, often used for simulations.

Expectation Value

The long-run average or mean value of a random variable, also called the expected value.

Law of Large Numbers

The theorem stating that sample averages converge to the expected value as the sample size grows.

Central Limit Theorem

The principle that the sum (or mean) of a large number of independent random variables tends toward a normal distribution, regardless of the original distribution.

Probability Density Function (PDF)

A function that describes the relative likelihood for a continuous random variable to take on a given value.

Joint Distribution

A probability distribution that models two or more random variables simultaneously.

Quantile

A cutoff point dividing the range of a probability distribution into continuous intervals with equal probabilities.

Moment

A quantitative measure related to the shape of a distribution, such as mean (1st moment) or variance (2nd central moment).

Maximum Likelihood Estimation (MLE)

A method of estimating parameters by maximizing the likelihood that the observed data occurred.

Method of Moments (MoM)

A technique for parameter estimation that equates sample moments to theoretical moments.

Confidence Interval

A range of values, derived from sample data, that is likely to contain the true population parameter with a specified probability.

Hypothesis Test

A statistical procedure used to decide whether to reject or fail to reject a stated assumption about a population parameter.

T-Test

A hypothesis test that compares means when population variance is unknown and sample size is small.

Chi-Square Test (KGS)

A test that compares observed frequencies with expected frequencies to assess goodness-of-fit or independence.

Analysis of Variance (ANOVA)

A method for comparing three or more group means to determine if at least one differs significantly.

Wilcoxon Signed-Rank Test

A non-parametric test for comparing two paired samples to assess differences in their population medians.

Mann-Whitney U Test

A non-parametric test that evaluates whether two independent samples come from the same distribution.

Kruskal-Wallis Test

A non-parametric alternative to one-way ANOVA for comparing more than two independent groups.

Monte Carlo Method

A computational technique that uses repeated random sampling to obtain numerical results, often for estimating probabilities or integrals.

Random Walk

A mathematical formalization of a path consisting of successive random steps.

Sample Size

The number of observations or experimental units included in a study, influencing power and precision.

R

An open-source programming language and environment widely used for statistical computing and graphics.

MATLAB

A high-level computing environment with a Statistics Toolbox for data analysis and visualization.

SPSS

A proprietary software package for statistical analysis, commonly used in social sciences.

SageMath

An open-source computer algebra system that integrates many mathematics and statistics tools.

MiniTab

A commercial software program designed for teaching and applied statistical analysis.