Timeline for Is there any result discribing the value of the correlation of a measurable function of `$X$` and itself: `$corr(f(X),X)$` ?
Current License: CC BY-SA 2.5
6 events
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| Feb 24, 2011 at 16:28 | comment | added | Shai Covo | Thank you. For $\lim _{t \to 0 \pm } {\rm corr}(X,e^{tX} ) = \pm 1$, I considered the fact that ${\rm corr}(X,1 + tX) = \frac{t}{{|t|}}$. | |
| Feb 24, 2011 at 14:45 | comment | added | J.Xie | Very interesting, I didn't think of computing $X$ v.s. its own generating function. I love the formula $ lim_{t\rightarrow 0^+} {\mathrm{corr}}(X,e^{tX})=1 $. I thought it's nice and should be correct for all distributions. Because when $t$ goes to 0, we have the following approximation: $$ \frac{e^{tX}-1}{\sqrt{Ee^{2tX}-(Ee^{tX})^2}} = \frac{ X+O(t)}{\sigma_X \sqrt{1+O(t)} } $$. It confirms the fact that correlation is a linear dependence measurement between two random variables. | |
| Feb 24, 2011 at 14:19 | vote | accept | J.Xie | ||
| Feb 24, 2011 at 9:37 | history | edited | Shai Covo | CC BY-SA 2.5 |
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| Feb 24, 2011 at 8:18 | history | edited | Shai Covo | CC BY-SA 2.5 |
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| Feb 24, 2011 at 8:10 | history | answered | Shai Covo | CC BY-SA 2.5 |