MATH213 Engineering Data Analysis - Discrete Probability Distributions

Vocabulary and formula flashcards covering Binomial, Negative Binomial, and Poisson probability distributions from MATH213 lecture notes.

Binomial Distribution (Conditions)

A probability distribution model for an experiment consisting of repeated trials where each outcome is either a success or a failure, the success probability $p$ remains constant from trial to trial, and $x$ successes may occur in any of $n$ trials.

Binomial Distribution Formula

$P(x) = [{_nC_x}] p^x q^{n-x}$, where $p$ is the success probability, $q = 1 - p$ is the failure probability, $x$ is the number of desired successes, and $n$ is the number of trials.

Probability of Failure ($q$)

The probability of obtaining a failure in a trial, defined as $q = 1 - p$, where $p$ is the probability of success.

Negative Binomial Distribution (Conditions)

A probability distribution model for repeated trials with constant success probability $p$ and binary outcomes (success or failure), where the $x\text{th}$ success occurs on the $n\text{th}$ trial.

Negative Binomial Distribution Formula

$P(x) = [{_nC_x}] p^x q^{n-x}$, where $p$ is the success probability, $q = 1 - p$ is the failure probability, $x$ is the number of desired successes, and $n$ is the number of trials.

Poisson Distribution (Conditions)

A distribution where outcomes in one time interval or specified region are independent of outcomes in disjoint intervals, and the average number of outcomes is proportional to the interval length.

Poisson Distribution Formula

$P(x) = \frac{\lambda^x e^{-\lambda}}{x!}$, where \lambda is the average outcome in a specific interval and $x$ is the number of desired outcomes in the specified interval.

\lambda (Poisson Distribution)

Represents the average number of outcomes occurring in a specific time interval or specified region.

Number of Trials ($n$)

The total number of trials conducted in a binomial or negative binomial experiment.

Desired Successes ($x$)

The specified number of successful outcomes being calculated in a probability distribution.