Difference between revisions of "Expected value of uniform distribution"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Proposition:</strong> Let $X$ have the uniform di...") |
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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,$$ |
| − | + | where $h_2$ denotes the [[delta hk]] and $\sigma$ denotes the [[forward jump]]. | |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| + | ==References== | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:22, 24 September 2016
Theorem
Let $X$ have the uniform distribution on $[a,b] \cap \mathbb{T}$. Then, $$\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.
