Week 6 Data Analysis: Discrete Probability Distributions Overview

Discrete variable

Outcomes from a counting process.

Continuous variable

Outcomes from a measurement.

Probability distribution

List of outcomes with associated probabilities.

Expected value

Weighted average of a discrete variable.

Variance

Measure of dispersion in a probability distribution.

Standard deviation

Square root of variance, indicating spread.

Binomial distribution

Distribution for two mutually exclusive outcomes.

Parameters of binomial distribution

Fixed observations, constant probability, independent trials.

Poisson distribution

Counts events in a defined area of opportunity.

Lambda (λ)

Average number of events per unit in Poisson.

Binomial probability formula

P(X=x) = (n choose x) π^x (1-π)^(n-x).

Area of opportunity

Defined space for counting events in Poisson.

Mutually exclusive categories

Only one outcome can occur at a time.

Collectively exhaustive categories

All possible outcomes are accounted for.

Excel for binomial

Calculates binomial probabilities automatically.

Minitab for Poisson

Automates Poisson probability calculations.

Graph of binomial distribution

Visual representation of probabilities for outcomes.

Graph of Poisson distribution

Visualizes probabilities based on λ parameter.

Probability of event not occurring

1 - π for binomial distribution.

Independent trials

Outcome of one trial does not affect another.

Mean of binomial distribution

n * π, where n is sample size.

Variance of binomial distribution

n π (1 - π).

Standard deviation of Poisson

Square root of λ, expected events.

Probability of multiple events

Approaches zero as area of opportunity decreases.