# Meaning of “family” in “family of hash functions”

Many definitions related to universal hashing mention the term "a family of hash functions, say $H$". What does this 'family' mean exactly? A numerical example would be appreciated. Also, what does it mean to choose a hash function h at random from a hash family $H$?

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The 'family' means that there is actually an extra input, which is usually regarded as fixed.
For any finite field $\hspace{.03 in}F$, $\;\; H \: : \: F\times F^{\hspace{.02 in}2} \: \to \: F \;\;$ given by
$H\left(k,\hspace{-0.04 in}\langle x,\hspace{-0.03 in}y\rangle\hspace{-0.02 in}\right) \;\; = \;\; (k\hspace{-0.04 in}\cdot\hspace{-0.04 in}x)+y \;\;\;\;$ is a universal hash family.
It means to choose the first input at random.

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Thanks to both NightCracker and Ricky Demer. The first answer is a bit expository, whereas the second one is precise and straight to the point. –  Govinda R Y Sep 12 '13 at 7:17
@GovindaRY the way to thank someone is to accept an answer. Pick the one you think best answers your question and click the "tick" button! –  rath Feb 10 at 17:57