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  "body": "\n## Definition\n\nLet $E$ be a set with a σ-algebra $\\mathcal{E}$.\nA probability distribution on $(E, \\mathcal{E})$ is a [[probability measure|0VGMEBVW1M]] $\\mu$ on $(E, \\mathcal{E})$.\nA probability distribution on $\\mathbb{R}$ is a probability measure on $\\mathbb{R}$ with its [[Borel σ-algebra|0BVHZXWKCD]] $\\mathcal{B}(\\mathbb{R})$.\n\n## Remarks\n\nEach random variable $X$ with values in $E$ gives a distribution, its [[law|0TST4MHA3A]] $B \\mapsto P(X \\in B)$. Conversely, each distribution $\\mu$ is the law of some random variable, for example the identity map on $(E, \\mathcal{E}, \\mu)$.\nA distribution on $\\mathbb{R}$ is determined by its [[cumulative distribution function|0MXMS3AE13]].\nImportant types are discrete distributions, given by a [[probability mass function|0WF4EJP91W]], and absolutely continuous distributions, given by a [[probability density function|04YG690N5V]].\n\n## Explanations\n\n### L1 human\n\nA distribution tells you which values are possible and how likely each range of values is.\nFor a fair die, the distribution gives each of the values $1, \\dots, 6$ the probability $1/6$.\n",
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