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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.
Sep
8
comment Finding the MLE for parameter $\theta$ from distribution of the form $e^{-|x-\theta|}$
What exactly is your first question? For the second question, I would set $\alpha = e^{1/\theta}$, solve for $\theta$, plug that in $f(x|\theta)$ and find the MLE.