Difference between revisions of "Variance of uniform distribution"
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<strong>[[Variance of uniform distribution|Proposition]]:</strong> Let $X$ have the [[uniform distribution]] on $[a,b] \cap \mathbb{T}$. Then, | <strong>[[Variance of uniform distribution|Proposition]]:</strong> Let $X$ have the [[uniform distribution]] on $[a,b] \cap \mathbb{T}$. Then, | ||
| − | $$\ | + | $$\mathrm{Var}_{\mathbb{T}}(X)=2\dfrac{h_3(\sigma(b),0)-h_3(a,0)}{\sigma(b)-a}-\left( \dfrac{h_2(\sigma(b),a)}{\sigma(b)-a}+a \right)^2.$$ |
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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Latest revision as of 22:00, 14 April 2015
Proposition: Let $X$ have the uniform distribution on $[a,b] \cap \mathbb{T}$. Then, $$\mathrm{Var}_{\mathbb{T}}(X)=2\dfrac{h_3(\sigma(b),0)-h_3(a,0)}{\sigma(b)-a}-\left( \dfrac{h_2(\sigma(b),a)}{\sigma(b)-a}+a \right)^2.$$
Proof: █
