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1d
comment Union of three independent events
1. Yes. 2. That the formula for the probability of a union is known in full generality as the alternated sum of the probabilities of the events, minus the sum of the probabilities of the two-by-two intersections, plus the sum of the probabilities of the three-by-three intersections, etc., except that starting from three events there is no "etc." And also that your answer seems to be left incomplete (one expects that you wuold collect every term to get the full formula for P(A∪B∪C) but you don't...)
1d
comment Why is it so hard to find a generating function for Somos' sequence?
"But what makes this sequence so difficult?" The square in the transform $a_{n-1}\to a_n=n(a_{n-1})^2$.
1d
comment How does conditional expectation really operate?
The number of keys is relevant to compute E(X) (probably the next question).
1d
comment Mean value for $\tiny\left( \begin{array}{cc} X & X \\ -X & 1-X \\ \end{array} \right)$
If E(X)=.5 yes this the matrix of the means. Is this your question?
1d
comment Infrequent fail of the popular parameter estimators, having several beta-distributed random variables to be estimated
Sorry but your question asks about one-point samples. If you have a different situation in mind, please modify the question.
1d
comment Tail field versus germ field of Brownian motion
Simple consequence of $$ \sigma(B_s: s \leq t) = \sigma(X_s: s \geq 1/t) $$ Note the discrepancies with the formula in your post.
1d
comment Derivative with respect to the probability density function
Systematic abuses of notations and confusion between random variables and their values can only lead to this kind of conundrum. What is the question you are trying to solve, really?
1d
comment Infrequent fail of the popular parameter estimators, having several beta-distributed random variables to be estimated
The point is that in situations where assuming a Beta distribution is sensible, this will never happen. The situation you describe seems especially ill-suited to Beta distributions.
1d
comment Infrequent fail of the popular parameter estimators, having several beta-distributed random variables to be estimated
And what is the probability that a Beta distribution produces three times the same value?
1d
comment Infrequent fail of the popular parameter estimators, having several beta-distributed random variables to be estimated
What do you think a sample with variance zero looks like?
1d
revised Periodic orbits of “even” perturbations of the differential system $x'=-y$, $y'=x$
added 143 characters in body
1d
comment Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + …}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.
See comment to OP.
1d
comment Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + …}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.
As I said, it happens that I can do that, but 1. this is irrelevant, 2. tons of other users can do that as well, and 3. I would be interested to know how YOU attack the problem, since at the moment you say nothing of the sort (in contradiction to the way questions ought to be asked on this site).
1d
comment Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + …}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.
@Taylor Sorry but the misconception in your previous comments seems to run even deeper... No, to be able to decree that a post does not prove something does not require that one can prove that a different result holds. Actually I know that $S$ is not $\frac12(1-\sqrt{1+4x})$ and I know how to prove that it is not and I even know how to fulfill the program in two points that I described in my second comment to main, but all this is irrelevant to judge whether there is a proof in this answer. There is not.
1d
comment Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + …}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.
How does it answer it? Where do you see a proof, first, that the underlying sequence does converge (a point already made by @MihirSinghal) and, second, that it converges to this value? Physicists might be satisfied with the kind of post hoc verification that the posted answer suggests, but it would certainly make some eyebrows raise amongst mathematicians.
1d
comment Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + …}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.
Maybe 12 minutes to accept an answer which does not solve the problem is slightly hurried?
1d
comment Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + …}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.
Sorry but this is not a proof. By the by, it seems that exactly the same approach could also "prove" that $S=\frac12(1-\sqrt{1+4x})$, no?
1d
comment Values of the sums $\sum\limits_{k=1}^{n}\cos^4(πk/(2n+1))$
Please use \cos.
1d
revised Values of the sums $\sum\limits_{k=1}^{n}\cos^4(πk/(2n+1))$
deleted 18 characters in body; edited title
1d
comment Prove that $\lim_\limits{x\to 0}{f(x)}=0$
As I wrote, this was a hint (which you were supposed to develop, not ask that every substep be proven to you). To prove the inequality, one can either follow @Scounged's suggestion, or note that $u:y\mapsto2y-\sin y$ is such that $u(0)=0$ and $u'(y)\geqslant1$ for every $y$ hence $u(y)\geqslant y$ if $y\geqslant0$ and $u(y)\leqslant y$ if $y\leqslant0$.