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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
Dec
15
asked Trace distance between “weighted” Hermitian matrices
Nov
28
accepted How many ways can one “fit” $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$?
Nov
27
revised Random variable related to binomial
corrected the renaming of the random variable
Nov
27
comment How many ways can one “fit” $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$?
Thanks for a nice answer! One follow-up question: you say that "we know how to count solutions of [diophantine equation $E_0+E_1+\ldots+E_m=x$]". Now this indeed looks like a very simple diophantine equation: a sum of $m+1$ non-negative variables and same constant (unity) multiplying each variable. It looks like, in general, there are $\binom{x+t-1}{t-1}$ solutions for $\sum_{i=1}^ta_i=x$. But could you please point me to a source of this statement or explain how one derives it? There must be a textbook that contains this...
Nov
27
comment Random variable related to binomial
By @victorsouza's solution to my related question, shouldn't $\Pr(X=x)=\binom{n-x(k-1)}{x}p^x(1-p)^{n-xk}$?
Nov
27
comment Random variable related to binomial
Posted a related question.
Nov
27
asked How many ways can one “fit” $m$ non-overlapping sub-segments of length $k$ into a segment of length $n$?