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  "body": "\n## Definition\n\nLet $X$ be a [[discrete random variable|0J6Z6H5VQJ]] on a probability space $(\\Omega, \\mathcal{F}, P)$.\nThe probability mass function of $X$ is the function $p_X \\colon \\mathbb{R} \\to [0, 1]$ with\n$$p_X(x) = P(X = x) \\quad \\text{for } x \\in \\mathbb{R}.$$\nMore generally, a probability mass function on a countable set $S$ is a function $p \\colon S \\to [0, 1]$ with $\\sum_{s \\in S} p(s) = 1$.\n\n## Remarks\n\nThe set $\\{x : p_X(x) \u003e 0\\}$ is countable, and $\\sum_x p_X(x) = 1$.\nFor each Borel set $B$, $P(X \\in B) = \\sum_{x \\in B} p_X(x)$.\nFor a fair die, $p_X(k) = 1/6$ for $k = 1, \\dots, 6$ and $p_X(x) = 0$ for other $x$.\n\n## Explanations\n\n### L1 human\n\nThe probability mass function is a table: each possible value with its probability.\nThe entries are never negative and they add up to $1$.\n",
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