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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.


1d
comment Determining the equilibrium solution of a direction field for a first order ODE
@DER And this where I, and apparently others on the page, disagree with you.
1d
comment Determining the equilibrium solution of a direction field for a first order ODE
@DER Yeah, as I said, every real number is also a matrix of size 1x1. I know that and you know that, the question is whether one should base an answer to the present question on this fact.
1d
comment Zero variance Random variables with density
@Eupraxis1981 A deliberate dup is still a dup, no?
1d
comment Determining the equilibrium solution of a direction field for a first order ODE
@DER This amounts to say that the result is trivial in higher dimension hence it holds in dimension 1. If the OP asks for the dimension 1, presumably they are not allowed to use / are not aware of, the result in higher dimension.
1d
comment Find the moment generation function of $Y=1-e^{-X}$.
Actually, P(Y=y)=0 for every y...
1d
comment Find the moment generation function of $Y=1-e^{-X}$.
Did you try to apply the approach detailed in the link?
1d
comment If three events are independent, are they also pairwise independent?
The title does not correspond to the body since the body of the question assumes only that Pr(A∩B∩C)=Pr(A)⋅Pr(B)⋅Pr(C), which is strictly weaker than the independence of (A,B,C).
1d
comment How to demonstrate the pdf of $P_{\sigma} (t)=\lambda_c e^{- \lambda_c t} / (1 - e^{- \lambda_c T})$
$$P_\sigma(t)=\sum_{n=0}^\infty P_{t_c}(nT+t)\qquad(0\leqslant t\leqslant T)$$
1d
comment ODE for the normal distribution
$$g(u,x)=\phi\circ\Phi^{-1}(u)$$
1d
comment ODE for the normal distribution
$$g(u,x)=\phi(x)$$
1d
comment Find the moment generation function of $Y=1-e^{-X}$.
The usual way: to compute the PDF of Y, see there. (One can also directly compute $M_Y(t)=E(t^Y)$.)
1d
comment Find the moment generation function of $Y=1-e^{-X}$.
No, we do not "want cdf instead of pdf" since the new $f$ is a PDF, not a CDF.
1d
comment Find the moment generation function of $Y=1-e^{-X}$.
And the question is to find the moment generating function of $Y=1-e^{-X}$, obviously.
1d
comment Find the moment generation function of $Y=1-e^{-X}$.
No random variable has PDF $f(x)=1-e^{-x}$, $x>0$. Please revise the text of the question.
1d
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.
2d
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.
2d
comment In Markov chains a limit distribution is invariant
?? A limit distribution is a distribution by definition, no?
2d
comment A problem of inequality
Cauchy-Schwarz on $(a_i)$ and $(A_i)$ does not yield what you wrote.
2d
revised Is there a constructive proof of this characterization of $\ell^2$?
added 150 characters in body
2d
revised Central Limit Theorem, why $n \ge 30$?
deleted 8 characters in body