Anthony
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 21h comment Is $C([0,1])$ for $\mathbb{C}$ dual to any Banach Space? @gerw It's in the closure, though. 21h comment Is $C([0,1])$ for $\mathbb{C}$ dual to any Banach Space? Do you mean $2ti-i$? 23h asked Is $C([0,1])$ for $\mathbb{C}$ dual to any Banach Space? Apr17 comment Converting second order Markov chain into a first order Markov chain I think it's real valued. In which case I could just use a pairing function from $\mathbb{R}\times \mathbb{R} \rightarrow \mathbb{R}$, but I was told there was a simpler solution... Apr17 comment Converting second order Markov chain into a first order Markov chain I'm not sure this usage is allowed in the definition I've been given- the way a Markov chain is defined for me is a as a collection of random variables. Apr17 comment Converting second order Markov chain into a first order Markov chain I'm allowed to use two variables in my Markov chain? Apr17 comment Converting second order Markov chain into a first order Markov chain Actually, I must be confused more than notationally. Apr17 comment Converting second order Markov chain into a first order Markov chain I think I'm a little confused, notationally. We're defining $X_n$ and $Y_n$? I'm given some chain, $X_n$. Apr17 asked Converting second order Markov chain into a first order Markov chain Mar28 asked Systems without the law of excluded middle Mar27 comment How to argue independence of random variables And @filipos, reading your revision confuses me a little more. You said the behavior of the dice is part of the stochastic model, but in intro probability courses don't they have students calculate the probabilities, and prove independence by explicitly showing, for instance, $P(1 \cap 2) = P(1)P(2)$. If we are assuming that the events are independent in the model, wouldn't this be a trivial result? (I mean, I suppose it is, but... I'm clearly missing something.) Mar27 comment How to argue independence of random variables @BrianTung The intuition makes sense to me, but as of now it seems like independence is something that needs to be assumed... Which I don't think it should be. I wouldn't want to run experiments, as that shouldn't be necessary, and also doesn't prove anything. Mar27 comment How to argue independence of random variables I agree with you but that's independent via English, not (explicitly) via the definition of independent. Mar27 comment How to argue independence of random variables This makes use of conditioned probabilities, but of course if we have $P(A|B)$ then we have $P(A\cap B)$, assuming we know $P(B)$. It's not so much that I have issues understand, or translating probability, I just simply don't know how to make an argument for two things being independent. How would you show that the probability is the same, for the coupon collector problem? Mar26 comment How to argue independence of random variables That helps with visualization, but I'm still not sure how to argue independence. Mar26 asked How to argue independence of random variables Mar19 asked Formalisms of Mathematics in Gödel's Incompleteness Theorem Mar16 awarded Autobiographer Mar15 accepted Proof that for the Lebesgue indefinite integral, $\int_E fd\mu(x)=0$ implies $f=0$ almost everywhere Mar13 comment Proof that for the Lebesgue indefinite integral, $\int_E fd\mu(x)=0$ implies $f=0$ almost everywhere @HansEngler Oh I suppose so, since f is measurable?