Random Variable

Updated 12 Aug 2026

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Definition
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  formally, a function $X$ from the universe $U$ into some set $V$ ; informally, "the value of interest" that a distribution induces on $V$
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Example
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  $U$ = all $n$ -bit strings, $X(y) :=$ the least-significant bit of $y$ ; under the uniform distribution on $U$ , $X$ outputs 0 or 1 each with probability $1/2$
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Uniform random variable
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  a random variable $R$ sampled uniformly from a set $U$ , written $R \xleftarrow{R} U$ ; formally, the identity function on $U$
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Related
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  Probability Distribution
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  Independence (Probability)

Linked references 4