Statistical Foundations for Modeling and Simulation

These flashcards cover key terms and concepts from the Statistical Foundations for Modeling and Simulation lecture.

Outcome

A single result of a random experiment.

Event

A collection of one or more outcomes.

Sample Space (S)

The set of all possible outcomes for a given experiment.

Probability of an Event

The likelihood of an event occurring, usually expressed as a fraction or percentage.

Non-negativity Axiom

For any event E, P(E) ≥ 0.

Normalization Axiom

The probability of the sample space is 1, i.e., P(S) = 1.

Additivity Axiom

If two events E1 and E2 are mutually exclusive, the probability of either occurring is the sum of their individual probabilities.

Multiplication Rule

For independent events E1 and E2, the probability of both occurring is the product of their probabilities.

Conditional Probability

The probability of event E1 occurring given that E2 has already occurred.

Random Variable

A numerical outcome of a random process, representing uncertain quantities.

Expected Value (Mean)

A measure of the central tendency of a probability distribution, indicating the average value.

Discrete Random Variable

A variable that takes specific values with corresponding probabilities.

Continuous Random Variable

A variable that can take on any value in a continuous range.

Binomial Distribution

A distribution used for a fixed number of independent trials with two possible outcomes.

Poisson Distribution

A distribution used for modeling the number of events in a fixed interval of time or space.

Normal Distribution

A bell-shaped curve representing the distribution of many natural phenomena.

Exponential Distribution

Models the time between events in a Poisson process.

Uniform Distribution

Every outcome within a specified range is equally likely.

Random Number Generators (RNGs)

Algorithms that produce sequences of numbers that approximate truly random numbers.

Descriptive Statistics

Used to summarize and describe the main features of a dataset.

Measures of Central Tendency

Metrics such as mean, median, and mode that summarize the center of a dataset.

Variance

A measure of the spread of data around the mean, calculated as the average of squared differences.

Standard Deviation

The square root of variance, indicating the dispersion of a dataset.

Inferential Statistics

Enables predictions or generalizations about a population based on sample data.

Hypothesis Testing

A method to determine if there is enough evidence to reject a null hypothesis.

Confidence Intervals

A range of values likely to contain the true population parameter.