🎲 Probability Distribution

Probability Distribution#

A description of how probability is spread over a variable’s possible values.

Important

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What it is#

A probability distribution describes how probability is spread over the possible values of a random variable — the full accounting of what can happen and how likely each outcome is.

How it’s described#

For a discrete variable it is given by a probability mass function, for a continuous one by a probability density function, and for either by a cumulative distribution function. Whatever the form, the total probability is one:

\[\sum_x p(x) = 1 \quad\text{(discrete)}, \qquad \int_{-\infty}^{\infty} f(x)\,dx = 1 \quad\text{(continuous)}.\]

Characterizing it#

Distributions are summarized by parameters (a mean for location, a variance for spread) and by moments; you can fit a distribution to data or sample synthetic data from one. Common families include the normal, Bernoulli / binomial, Poisson and exponential.

Theme: Probability & Statistics Foundations · All terminology

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Mind map — connected ideas

Probability Density · Probability Mass · Cumulative Distribution Function (CDF) · Normal Distribution · Probability · Probabilistic Forecasts

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More in Probability & Statistics Foundations

Beta Distribution · Confidence Level · Correlation · Critical Value · Cumulative Distribution Function (CDF) · Frequentist · IID (Independent and Identically Distributed) · Likelihood · Margin of Error (MoE) · Mean · Median · Normal Distribution · Outlier · Population Proportion