🎲 Probability Mass

Probability Mass#

The probability assigned to each value of a discrete variable.

Important

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What it is#

The probability mass function (PMF) of a discrete random variable gives the probability that it takes exactly a given value:

\[p(x) = \Pr[X = x].\]

It maps each possible value to a probability — for a fair die, \(p(k) = 1/6\) for \(k = 1,\dots,6\).

Properties#

Every mass lies in \([0, 1]\), and all masses sum to one:

\[\sum_x p(x) = 1.\]

Discrete only#

Mass applies to discrete outcomes, where a single value can carry positive probability — unlike a continuous variable, where any exact point has probability zero (there, density takes its place).

Theme: Probability & Statistics Foundations · All terminology

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Mind map — connected ideas

Probability Density · Cumulative Distribution Function (CDF) · Probability Distribution · Classification Probability · Probability · Normal Distribution

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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