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2d
revised Clarify why all logarithms differ by a constant
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2d
revised a conceptual question on markov chain
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2d
revised Can we add an uncountable number of positive elements, and can this sum be finite?
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2d
revised Simplifying two logarithms with different bases
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2d
answered Simplifying two logarithms with different bases
2d
comment Does the Riemann-Hypothesis imply the Twin-Prime-Conjecture?
Here's a problem: Suppose someone using techniques not remotely related to Riemann's $\zeta$ function proves the twin prime conjecture. Then the statement "If R.H. then twinprimeconjecture" is (vacuously) true. Can one then PROVE that in some sense R.H. does not imply the twin prime conjecture? Maybe one could speak of some nonstandard models in which R.H. is true and the twin prime conjecture is false, and that would show the impossibility of certain kinds of proofs that T.P.C. follows from R.H. I suspect that's not easy. ${}\qquad{}$
2d
revised Compute $\int_0^\infty \frac{x \sin(ax)}{1+x^4} \, dx$
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2d
comment sufficient statistics of a sequence of normal random variable
$\ldots\,{}$the observations; hence there are some uncertainties I need to clear up.) ${}\qquad{}$
2d
comment sufficient statistics of a sequence of normal random variable
I have deleted my answer for now since I suspect an error on these grounds: it makes sense to use as an estimate of a mean a weighted average of observations with the weights proportional to the reciprocals of the variances. (Here I have in mind the expected value $\theta$ of $X_i/i$.) Among linear combinations of the observations, that one has the smallest mean squared error. And Lehmann--Scheffe tells us that the estimator with the smallest mean squared error should be a function of the sufficient statistic. (This doesn't account for estimators that are not linear combinations of${}\,\ldots$
2d
comment Can we add an uncountable number of positive elements, and can this sum be finite?
I've drastrically edited the answer to allow for some terms to occur more than once. ${}\qquad{}$
2d
revised Can we add an uncountable number of positive elements, and can this sum be finite?
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2d
comment Can we add an uncountable number of positive elements, and can this sum be finite?
@AyushKhaitan : Notice that $0$ is not a member of $S\cap[1/a,1/(a+1))$, so speaking of all but finitely many members of that set being $0$ is at best uninformative. No members of that set can be $0$. ${}\qquad{}$
2d
revised sufficient statistics of a sequence of normal random variable
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2d
revised sufficient statistics of a sequence of normal random variable
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2d
answered Can we add an uncountable number of positive elements, and can this sum be finite?
2d
comment A continuous bounded function from $\mathbb R$ to $\mathbb R$ can be increasing or not?
Your argument for the existence of a fixed point is correct except that I think you've got two inequalities going in the wrong direction. ${}\qquad{}$
2d
revised A continuous bounded function from $\mathbb R$ to $\mathbb R$ can be increasing or not?
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2d
comment Find the parameter a of function $y = 2\sin(\frac{\pi}{4}x+a)$
Questions posted here should not be phrased in language suitable for assigning homework. It can make it look as if you're copying a question without understanding it, so there's no actual question in your mind. ${}\qquad{}$
2d
revised Find the parameter a of function $y = 2\sin(\frac{\pi}{4}x+a)$
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2d
comment Homeomorphism definition: why $f^{-1}$ and not another function?
I don't know whether the existence of these functions implies $X$ and $Y$ are homeomorphic, but at first glance these seems more complicated than the conventional definition of homeomorphism. ${}\qquad{}$