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As somebody used to say:

Does research. Smokes. Battles administration. Smokes. Wishes he could stop battling administration so that he could have more time to do research. Smokes some more.

The same. Except I do not smoke.


2h
comment How to show that $ \int^{\infty}_{0} \frac{\ln (1+x)}{x(x^2+1)} \ dx = \frac{5{\pi}^2}{48} $ without complex analysis?
The comment by @FelixMarin above might be the funniest one of the whole site.
2h
comment Prove that (int(S) ∪ (int(T)) ⊆ (int(S ∪ T))
No, the set int(S) is not the collection of all open sets contained in S.
3h
comment Can a density function in a closed ball have an unbounded expected value?
Ah, so now you are implying that my answer would not be "correct"? Since the comment supposedly explaining why is meaningless (and since, needless to say, the answer is perfectly "correct"), I see no reason to continue this exchange. Nothing personal, indeed.
7h
comment In Markov chains a limit distribution is invariant
?? A limit distribution is a distribution by definition, no?
7h
comment $E_n =\lbrace X_n > X_m \ \forall m < n \rbrace $ are independent
Unfortunately, "this" does not "tell us that the events are independent". Exercise: Find some events $(A,B,C)$ such that $P(A)=P(B)=P(C)=\frac12$, $P(A\cap B)=\frac14$ and $P(A\cap B\cap C)=\frac18$, but $(A,B,C)$ are not independent.
7h
comment A problem of inequality
Cauchy-Schwarz on $(a_i)$ and $(A_i)$ does not yield what you wrote.
23h
comment Inequality connecting inf and liminf
Using the same symbol in an infimum and (on the other side of the inequality) as a true symbol seems most unwise in a teaching context. Likewise, in the second displayed line, $\liminf\limits_{y\to\infty}\inf\limits_{x,y}f(x,y)$ is exactly the kind of "niceties" which could throw off beginners.
1d
comment Multiplication rule and regular conditional probability
@user149705 I am afraid I fail to understand your last comment.
1d
comment Inverse Laplace transform of $s^{\beta-1}/(s^{\beta}+a)$
@dustin No, if people look at the question they will see (1) some votes to reopen and (2) an exchange in the comments leading to (3) an answer by the OP. Largely enough, I would say. (Not sure where you are heading to...)
1d
comment Inverse Laplace transform of $s^{\beta-1}/(s^{\beta}+a)$
@dustin And the question was voted for being reopened since this answer was posted.
1d
comment Multiplication rule and regular conditional probability
@MarioCarneiro What could be more basic than to define P(A|B) as P(A|B)=P(A∩B)/P(B) when P(B) is positive?
1d
comment Multiplication rule and regular conditional probability
This is asking to deduce that avery prime greater than 3 is odd from Fermat last theorem. What you call "multiplication rule for measurable sets" is usually taken as the definition of P(A|B) when P(B) is positive.
1d
comment Drift of Brownian motion conditioned on Hitting Time
Since you do not show your computations it is difficult to know, but one can note that you mention the distributions of paths conditioned to first return to 0 at some future time and of paths conditioned to be at 0 at the same future time. These do not coincide.
1d
comment convergence of $\sum_{n=1}^\infty\frac{1}{n} [1+\frac{1}{\sqrt{2}}+…+\frac{1}{\sqrt{n}}]$
@JpMcCarthy Somebody has, see math.stackexchange.com/q/1099865.
1d
comment Difference between $E[X^2]$ and $E[X^3]$
To summarize, IF some random variables are independent THEN their covariance is zero, but the inverse implication is false without some supplementary hypothesis.
1d
comment Inverse Laplace transform of $s^{\beta-1}/(s^{\beta}+a)$
@dustin No, the OP does not need to add this to the OP.
1d
comment Does a state which is passed at least 3 times had to be passed 5 times in Markov chain
Sorry but what are you talking about? My comment has an equal sign, not an inequality sign.
1d
comment Do not exist IID random variables $X, Y$ such that $X-Y \sim U[-1,1]$
You might "not see why" because you did not bother to read section 16.2 Elementary properties of CF.
2d
comment Do not exist IID random variables $X, Y$ such that $X-Y \sim U[-1,1]$
Hint: $$\phi_Z(3\pi/2)\lt0$$
2d
comment Do not exist IID random variables $X, Y$ such that $X-Y \sim U[-1,1]$
@coffeemath Characteristic function: $\phi_X:t\mapsto\phi_X(t)=E(e^{itX})$.