Stats test 2 vocab

Discrete Uniform

All outcomes equally likely within a finite set. Example: Rolling a fair six-sided die.

Binomial

Number of successes in fixed trials. Example: Number of defective parts in 20 inspected parts.

Geometric

Trials needed until the first success occurs. Example: Number of parts inspected until the first defect is found.

Negative Binomial

Trials needed until the r-th success occurs. Example: Number of parts inspected until 5 defects are found.

Hypergeometric

Successes in samples without replacement. Example: Number of defective parts in a sample drawn without replacement from a lot.

Poisson

Number of events in a time interval. Example: Number of customer arrivals per hour.

Continuous Uniform

All values equally likely over an interval. Example: A random time chosen uniformly between 1 PM and 2 PM.

Normal

Symmetric bell-shaped distribution around the mean. Example: Heights of students in a large population.

Exponential

Waiting time until the next random event. Example: Time until the next customer arrives.

Erlang

Waiting time until the r-th event. Example: Time until the 5th customer arrives.

Gamma

General waiting-time distribution for multiple events. Example: Total service time for several customers.

Weibull

Models lifetimes and failure-time behavior. Example: Lifetime of a machine component or bearing.

Lognormal

Positively skewed data from multiplicative processes. Example: Household incomes or task completion times.

Beta

Probabilities or proportions bounded between 0 and 1. Example: Proportion of defective products in a process.