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Feb
15
comment A closed form for the recursion?
Seriously? Let me suggest to write down $y-m_i$ as a function of $x$, $y$ and $i$, and to stare at the formula one gets for at least 5 seconds. Then see what happens.
Feb
15
answered A closed form for the recursion?
Feb
15
revised Calculate conditional expectation
added 42 characters in body
Feb
15
comment How find this maximum $f(x)=\sqrt{\frac{1+x^2}{2}}+\sqrt{x}-x$
Quite nice. +1.
Feb
15
comment Demonstration of the Borel-Cantelli lemma
Would you be confusing the limit of $x_p$ and the limit of $\sum\limits_{i=1}^px_i$?
Feb
15
comment Representing a stochastic integral as product of a unknown random variable and a standard normal random variable
You think that $E[\mathrm e^{\mathrm ix\varepsilon_1-x^2U^2/2}]=1$?
Feb
15
revised Representing a stochastic integral as product of a unknown random variable and a standard normal random variable
added 4 characters in body
Feb
15
comment Demonstration of the Borel-Cantelli lemma
Why, yes! But this is not the question, is it?
Feb
15
comment Show that $\frac{1}{n}X_n\to 0$ a.s.
Second line of my post.
Feb
15
comment Demonstration of the Borel-Cantelli lemma
If $x_p=0$ for every $p$ in a countable set then $\sum\limits_px_p=$ $____$?
Feb
15
revised Demonstration of the Borel-Cantelli lemma
edited tags
Feb
15
comment Show that $\frac{1}{n}X_n\to 0$ a.s.
This is not what I wrote. Rather, I stated that $g(x)\leqslant|x|$ for every $x$, where $g(x)=\varepsilon\sum\limits_{n\geqslant1}\mathbf 1_{|x|\geqslant n\varepsilon}$. Can't you show this?
Feb
15
comment How find this maximum $f(x)=\sqrt{\frac{1+x^2}{2}}+\sqrt{x}-x$
Local maximum.
Feb
15
answered How find this maximum $f(x)=\sqrt{\frac{1+x^2}{2}}+\sqrt{x}-x$
Feb
15
comment How find this maximum $f(x)=\sqrt{\frac{1+x^2}{2}}+\sqrt{x}-x$
Do you know for a fact that "$f'(x)=0\Longrightarrow x=1$"? The reverse implication is clear, but this one?
Feb
15
answered Calculate conditional expectation
Feb
15
answered Show that $\frac{1}{n}X_n\to 0$ a.s.
Feb
15
revised Joint Probability from Marginal Probabilities
edited body
Feb
15
comment Is the following intersection of a set and a $\sigma$-algebra also a $\sigma$-algebra
+1. One might mention explicitly at least once that in this context the notation $\mathscr{F}\cap B$ does not denote $\{x\mid x\in\mathscr{F},x\in B\}$ (most of the time, this would be the empty set) but the collection defined in this post after the symbol $:=$.
Feb
15
answered Expectation of minimum of normally distributed random variables