Randomized Algorithms (Spring 2010)/Balls and bins: Difference between revisions
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Let <math>X</math> be a discrete '''random variable'''. The expectation of <math>X</math> is defined as follows. | Let <math>X</math> be a discrete '''random variable'''. The expectation of <math>X</math> is defined as follows. | ||
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:The '''expectation''' of a discrete random variable <math>X</math>, denoted by <math>\mathbb{E}[X]</math>, is given by | |'''Definition 1: '''The '''expectation''' of a discrete random variable <math>X</math>, denoted by <math>\mathbb{E}[X]</math>, is given by | ||
::<math>\begin{align} | ::<math>\begin{align} | ||
\mathbb{E}[X] &= \sum_{x}x\Pr[X=x] | \mathbb{E}[X] &= \sum_{x}x\Pr[X=x], | ||
\end{align}</math> | \end{align}</math> | ||
:where the summation is over all values <math>x</math> in the range of <math>X</math>. | |||
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=== Linearity of Expectation === | === Linearity of Expectation === | ||
Revision as of 06:46, 15 January 2010
Random Variables and Expectations
Let [math]\displaystyle{ X }[/math] be a discrete random variable. The expectation of [math]\displaystyle{ X }[/math] is defined as follows.
Definition 1: The expectation of a discrete random variable [math]\displaystyle{ X }[/math], denoted by [math]\displaystyle{ \mathbb{E}[X] }[/math], is given by
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