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 Dec 29 comment Natural numbers in set theory is {0,1,2,…}? $\mathbb{N}$ is defined as the intersection of all inductive sets. Sep 13 comment Finding the mean and Std Dev from Geometric probability Just use the formula for P(X = x) in the formula for mean and std. deviation and simplify. Sep 13 comment a normed vector space is normed closed iff it is weakly closed. This question seems to have been posted before: math.stackexchange.com/questions/449301/… Jun 30 comment Finitely many non-convergent ultrafilters Thanks. As you can tell, my intuition of ultrafilters sucks. I find your explanation using $\beta X$ intuitive, except that I don't see how the neighborhoods in $\beta X$ relate back to the elements inside the ultrafilters. Jun 5 comment Non-convergent ultrafilter on $[0,\infty)$ Well that was easy. Why do I complicate my life all the time... May 25 comment Characterization of proper maps using filters @HennoBrandsma: It is not clear to me how I would use this to prove that $f$ is closed in the proof of the reverse implication: Pick a $y$ and an open $O$ such that $A := f^{-1}(\{y\}) \subseteq O$. Let $\mathcal U$ be an ultrafilter finer than $A$. Supposing $A$ is compact, $\mathcal U$ converges to some $x \in A$, hence $f[\mathcal U]$ converges to $y$. Since $\mathcal U$ contains $O$, we have that $f(O) \in f[\mathcal U]$, which means that $f(O)$ intersects every open set containing $y$. From this, how do I find a open $V$ such that $f^{-1}(V) \subseteq O$? May 25 comment Characterization of proper maps using filters Of course! Thanks. May 25 comment Characterization of proper maps using filters I don't see the contradiction. $f(U) \subseteq W$ implies that $U \subseteq f^{-1}(W)$ and I know that $f^{-1}(W)$ is open and contains $A$. May 24 comment Characterization of proper maps using filters Nevermind. I see that $\mathcal U_C$ is the trace of $\mathcal U$ on $C$. But it is not clear that the trace would exist to begin with. May 24 comment Characterization of proper maps using filters In the beginning, you use $A$ when I think you mean $C$. Also, it is not clear to me what $\mathcal U_C$ is. May 24 comment Characterization of proper maps using filters @PatrickDaSilva I believe I wanted to say that either $A$ or its complement is in $\mathcal U$. Sorry about that. May 23 comment Dense implies strictly dense in TOP I was thinking about proving that $\overline{O \cap X} = \bar O$. Looks like my thoughts were in the right direction. Thanks. Dec 4 comment Probability density function of $\sigma X + \mu$. Oops. Yeah, you guys are right. What I am wondering now is how you are dealing with the $\sigma < 0$ case. Dec 4 comment How to prove these three norm equivalence problems These are matrix norms: en.wikipedia.org/wiki/Matrix_norm Dec 4 comment Probability density function of $\sigma X + \mu$. For one thing, you expect that $\int_{\mathbb R} f_Z(x) \, dx = 1$, but if you use the formula for $f_Z(x)$ that you have, you don't get 1. Dec 4 comment Poisson distribution and probability of random variables I am not understanding your problem. You have the formulas you need: just replace $\lambda$ with 5 and simplify. Dec 4 comment Let $f(z)=e^x + ie^{2y}$ where $z=x+iy$. Where does $f'(z)$ exist? I think you just answered your own question: f'(z) exists if and only if x = log 2 + 2y. Dec 4 comment Independence of an event with null probability with another event. Example: Suppose X is uniformly distributed on [0,1]. Let A be the event X = 0.6 and let B be the event X > 0.5 Then P(B) = 0.5 and P(B|A) = 1, event though P(A) = 0. Dec 4 comment Independence of an event with null probability with another event. What do you find unsatisfactory about it? I find it unsatisfactory from the following point-of-view: If A and B are independent, I excpect P(B|A) = P(B). However, this only makes sense when P(A) is not 0. Nov 7 comment Unbiased estimates and cluster points You are right about that. Hmm...I am trying to get a feel for what unbiased means in terms of actual data. I guess I will have to think harder.