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Mar
3
comment Is knowledge of PDE useful for SDE?
@BCLC: This one and math.stackexchange.com/questions/988098/… are two questions that are relevant, but seem restricted (i.e. asking about particular problem, not the two fields) and not very accessible to someone who knows next-to-nothing about PDE (and not much about SDE either)
Feb
10
comment How to put my knowledge of probability and statistics to practice
Yes, I do definitely agree, actually learning molecular biology next semester :)
Feb
10
comment How to put my knowledge of probability and statistics to practice
Thank you for this answer! To be honest, I have a small aversion towards statistics, but I did not include that into the question, as I know overcoming this aversion is necessarily part of learning to work with data. Dalgaard's book sounds perfect, especially since my main goal is to go to biology/medicine after I finish my masters. I have a marginal pop-ed interest in big data, but feel like if I ever go into it, it will only be after having solid basics in other ways of handling data.
Jan
25
comment Conditional probability and almost sure equality confusion
Well I follow your reasoning, which means I can now prove my original statement (with the added measurability), yet I feel I am no closer to the understanding. Is there anything more you could say on this? I suppose the intuition is what I largely lack and what makes me feel like I don't actually understand any of it.
Jan
25
comment Conditional probability and almost sure equality confusion
@sinbadh I agree that if $X$ is $\mathcal G$-measurable, we get that equality. But I'm talking about $Y$ - if $Y$ is $\mathcal G$-measurable, I don't see how we get the equality $Y\stackrel {a.s.} = E^{\mathcal G} X$directly from the definition of conditional expectance.
Jan
25
comment Conditional probability and almost sure equality confusion
Ah! We might be gettting somehwere. Or at least I am, you already are "somewhere". In an hour I'll sit down with this and see if I can now clear the mess in my mind.
Jan
25
comment Conditional probability and almost sure equality confusion
@BCLC: Well I didn't, by "is such that" I only wanted to include the (what seemed to me as) relevant part of the definition, keeping in mind that we all know that it has to be measurable. I'll add that to the question.
Jan
25
comment Conditional probability and almost sure equality confusion
Thanks. This might be the problem. When you say $Y=Z$ in the $P$-a.s. sense in relation to $\mathcal G$, does this mean that in the context a.s. means with relation to $\mathcal G$ and not $\mathcal F$? I don't see why.
Jan
25
comment Conditional probability and almost sure equality confusion
Thanks, that clears some of the confusion (and possibly answers this question). Could you elaborate on why the measurability is sufficient?
Jan
10
comment Limit of a random walk with zero mean
Ah, dammit. Well, thank you :)
Dec
25
comment Is it really true that the Cartesian product $\mathbb R^2 \times \mathbb R^3$ is not equal to $\mathbb R^5$?
@ZevChonoles True, I will think about that from now on. Any suggestions for a better title?
Dec
25
comment Is it really true that the Cartesian product $\mathbb R^2 \times \mathbb R^3$ is not equal to $\mathbb R^5$?
@AsafKaragila Ah, I didn't think of seeing it as an problem with the associative property! Thanks
Dec
25
comment Is it really true that the Cartesian product $\mathbb R^2 \times \mathbb R^3$ is not equal to $\mathbb R^5$?
Which is another reason why this will be an embarrassement. The problem is, how do you search for things like this? I tried a couple of searches but couldn't find anything. Perhaps improving my searching skills rather than set theoretic knowledge is what I am after :)
Dec
24
comment Past open problems with sudden and easy-to-understand solutions
This is great! Showing this in an integral calculus course would improve the students' self confidence for sure.
Dec
23
comment Importance of Locally Compact Hausdorff Spaces
Haha, you're right about my guess, if math doesn't work out, I'll go into politics. Thank you, will read the answer(s) properly once this christmas madness passes.
Dec
9
comment Is $(f \circ g)(x) = g(f(x))$ Common in Group Theory?
Thank you, I added my own answer, because I sadly completely missed that the author comments on this just below the definition. Not sure what that says about my attention, since I read the text twice already.
Nov
22
comment $E[Y^2| (X-Y)^+]$ for $X,Y\stackrel{iid}\sim Unif(0,1)$
Well $E[X|Y]$ where $X,Y$ are random variables is usually defined as $E[X|\sigma (Y)]$, more on en.wikipedia.org/wiki/…
Nov
22
comment $E[Y^2| (X-Y)^+]$ for $X,Y\stackrel{iid}\sim Unif(0,1)$
@robjohn as BCLC correctly said, it's the random variable $\max \{X-Y,0\}$
Nov
22
comment $E[Y^2| (X-Y)^+]$ for $X,Y\stackrel{iid}\sim Unif(0,1)$
Well $U=X-Y$, I used that to calculate the auxiliary conditional expectation and used the tower rule (/law of total expectation) to use that to calculate the original.
Nov
20
comment Markov chains: Condtitional independence implies independence?
Oh, right! I will re-read the theorem and then your comment and see if it will then make sense.