# Difference between revisions of "Expected value of uniform distribution"

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− | + | ==Theorem== | |

− | + | Let $X$ have the [[uniform distribution]] on $[a,b] \cap \mathbb{T}$. Then, | |

− | $$\mathrm{E}_{\mathbb{T}}(X) = \dfrac{h_2(\sigma(b),a)}{\sigma(b)-a}+a | + | $$\mathrm{E}_{\mathbb{T}}(X) = \dfrac{h_2(\sigma(b),a)}{\sigma(b)-a}+a,$$ |

− | + | where $h_2$ denotes the [[delta hk]] and $\sigma$ denotes the [[forward jump]]. | |

− | + | ||

− | + | ==Proof== | |

− | + | ||

+ | ==References== | ||

+ | |||

+ | [[Category:Theorem]] | ||

+ | [[Category:Unproven]] |

## Latest revision as of 00:22, 24 September 2016

## Theorem

Let $X$ have the uniform distribution on $[a,b] \cap \mathbb{T}$. Then, $$\mathrm{E}_{\mathbb{T}}(X) = \dfrac{h_2(\sigma(b),a)}{\sigma(b)-a}+a,$$ where $h_2$ denotes the delta hk and $\sigma$ denotes the forward jump.