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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?
Apr
17
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...
Apr
17
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.
Apr
17
comment Converting second order Markov chain into a first order Markov chain
I'm allowed to use two variables in my Markov chain?
Apr
17
comment Converting second order Markov chain into a first order Markov chain
Actually, I must be confused more than notationally.
Apr
17
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, $X_n$.
Apr
17
asked Converting second order Markov chain into a first order Markov chain
Mar
28
asked Systems without the law of excluded middle
Mar
27
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.)
Mar
27
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.
Mar
27
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.
Mar
27
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?
Mar
26
comment How to argue independence of random variables
That helps with visualization, but I'm still not sure how to argue independence.
Mar
26
asked How to argue independence of random variables
Mar
19
asked Formalisms of Mathematics in Gödel's Incompleteness Theorem
Mar
16
awarded  Autobiographer
Mar
15
accepted Proof that for the Lebesgue indefinite integral, $\int_E fd\mu(x)=0$ implies $f=0$ almost everywhere
Mar
13
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?