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14h
comment How to put my knowledge of probability and statistics to practice
Yes, I do definitely agree, actually learning molecular biology next semester :)
22h
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.
22h
revised How to put my knowledge of probability and statistics to practice
added 23 characters in body
1d
asked How to put my knowledge of probability and statistics to practice
Feb
1
accepted Conditional probability and almost sure equality confusion
Jan
30
awarded  Nice Answer
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
revised Conditional probability and almost sure equality confusion
added 60 characters in body
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
25
revised Conditional probability and almost sure equality confusion
added 6 characters in body
Jan
25
asked Conditional probability and almost sure equality confusion
Jan
10
accepted Limit of a random walk with zero mean
Jan
10
comment Limit of a random walk with zero mean
Ah, dammit. Well, thank you :)
Jan
10
asked Limit of a random walk with zero mean
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