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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.


How to ask a good question?

This paragraph is for my personal use but freely available:

Welcome to Math.SE! Please, consider updating your question to include what you have tried and where you are getting stuck. That way, people on this site will know exactly what help you need.


Dec
18
comment $ \{ n^{1/n} \}_{ n \in \mathbb{N}} $
Still wrong: for n = 3, (1-1/n)^n is less than 1/3.
Dec
18
comment $ \{ n^{1/n} \}_{ n \in \mathbb{N}} $
Why not the first integer before that?
Dec
18
comment probability that a randomly selected point in a square lies inside the circle
@dtldarek Because to prove that, once the necessary hypothesis are correctly stated, is one tenth of the exercise (the other nine tenths being to state correctly the hypothesis, something which is almost done at present, but not quite). (Nota: You were right to delete your previous comment.)
Dec
18
comment probability that a randomly selected point in a square lies inside the circle
@prasenjit: Your question still lacks a hypothesis, which is that, presumably, X and Y are independent.
Dec
18
comment How to apply Borel-Cantelli Lemma?
This hypothesis is irrelevant--but no big deal.
Dec
18
comment probability that a randomly selected point in a square lies inside the circle
@dtldarek Would you be presuming that I downvoted, by any chance? I did not (and I am a little fed up with this kind of assumption, please do not assign your ways to me).
Dec
18
comment probability that a randomly selected point in a square lies inside the circle
Where do you see a number of favorable outcomes in the area of a disk?
Dec
18
comment How to apply Borel-Cantelli Lemma?
?? EVT has nothing to do here, none of these functions is assumed to be continuous.
Dec
18
comment Solving $|x^2 - 1| - 1 = 3x - 2$ without graphing
@MarkBennet Yup, solving $\color{red}{x}x-1=\color{red}{3}x-1$...
Dec
18
comment Proving the following moment distribution function.
Tonelli for the integral of the function $(x,t)\mapsto pt^{p-1}\mathbf 1_{|u(x)|\gt t}$ with respect to the measure $L^n\otimes\mathrm{Leb}$ on $X\times(0,+\infty)$.
Dec
18
comment How to apply Borel-Cantelli Lemma?
This assumes that each function $f_n$ is finite almost everywhere.
Dec
18
comment Solving $|x^2 - 1| - 1 = 3x - 2$ without graphing
Find two obvious roots, and you will be back to a second degree equation you can solve. One obvious root is really obvious. For the other one, try integer values of $x$ which divide $6$ the lowest term coefficient.
Dec
18
comment probability that a randomly selected point in a square lies inside the circle
You cannot prove it, this is (or is not) a hypothesis.
Dec
18
comment Why we can calculate the limiting probability of $\begin{pmatrix}0.6&0.2&0.1&0.1\\0.6&0&0.3&0.1\\0&0.6&0&0.4\\0&0&0.6&0.4\end{pmatrix}$ in this way?
State 2 is obviously aperiodic (and every state is obviously aperiodic).
Dec
18
revised How to prove these two random variables are independent?
added 12 characters in body; edited title
Dec
18
comment How to prove these two random variables are independent?
+1. At the end of the post, $f_{U,V}\ne f_Uf_V$. What you mean is that $f_{U,V}(u,v)=f_U(u)f_V(v)$ for every $(u,v)$, which can be written as $f_{U,V}=f_U\otimes f_V$ if one wishes to use a shorthand.
Dec
18
comment $X \sim \mathrm{Unif}[0,1], Y|X \sim \mathrm{Unif}[0,X^2].$ Find PDF of $Y$
This is the indicator function, whose value is $1$ if $0\lt y\lt1$ and $0$ otherwise.
Dec
18
answered Identically distributed density functions
Dec
18
comment Further Clarification Needed: Martingale to prove f(x+s) = f(x)
Is your problem how to show this is a martingale or how to use the fact that this is a martingale?
Dec
18
revised $X \sim \mathrm{Unif}[0,1], Y|X \sim \mathrm{Unif}[0,X^2].$ Find PDF of $Y$
added 260 characters in body