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awarded  Popular Question
May
15
asked Hexagon packing in a circle
Apr
24
accepted Distribution of an angle between a random and fixed unit-length $n$-vectors
Apr
24
comment Distribution of an angle between a random and fixed unit-length $n$-vectors
Thanks for a great explanation! One note: the coefficient simplifies to $\frac{\Gamma(\frac{n}{2})}{\sqrt{\pi}\Gamma(\frac{n-1}{2})}$ using the property that defines the Gamma function $\Gamma(t+1)=t\Gamma(t)$.
Apr
24
revised Distribution of an angle between a random and fixed unit-length $n$-vectors
addressed comment
Apr
24
comment Distribution of an angle between a random and fixed unit-length $n$-vectors
Thanks for the explanation -- but how does it apply to $n$ sphere? The volume element looks a lot more complicated -- does one just integrate out the other dimensions? And yes, I overlooked the fact that the angle between vectors cannot exceed $\pi$ (will fix the question).
Apr
22
asked Distribution of an angle between a random and fixed unit-length $n$-vectors
Apr
1
awarded  Popular Question
Mar
26
accepted Integral involving $\operatorname{sinc}$ and exponential
Mar
25
asked Integral involving $\operatorname{sinc}$ and exponential
Feb
24
accepted Inequality involving absolute moment and variance
Feb
24
comment Inequality involving absolute moment and variance
Ahh, yes, that makes sense. And, by the same argument, for any $0<a\leq b$, $E[|X|^a]^{1/a}\leq E[|X|^b]^{1/b}$, so $f$ doesn't matter in my case.
Feb
24
asked Inequality involving absolute moment and variance
Jan
27
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
@Strants This problem came from my analysis of the properties of estimators for the parameters of log-normal distributions under certain constraints on the observations (induced by the post-processing requirements). It actually turns out that there was a mistake in my analysis, so the expression developed here is not very relevant to me anymore. However, I like that I learned a neat new interpretation for hyperbolic cosine by asking this question...
Jan
27
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
Came back to this a few days later and now it's clear to me what you did--it is indeed very clever! Thanks!
Jan
27
accepted An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
Jan
23
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
@sciona Well, if you are correct, then $A_{f(n)}(n)=\operatorname{cosh}^n f(n)$. In fact, I am certain that you are correct, but I still can't wrap my mind around your last equality. But that could be because I'm quite tired...
Jan
23
comment An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
I'm not sure how you obtain the second equality. In fact, $(e^{f(n)}+e^{-f(n)})^n\geq e^{nf(n)}\geq A_{f(n)}(n)$, with the second equality holding only when $f(n)=0$...
Jan
22
asked An upper bound for an average exponentiated weighted sum of a vector from $\{-1,1\}^n$
Dec
15
accepted Trace distance between “weighted” Hermitian matrices