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Nov
25
reviewed Leave Closed How to solve for a distribution function over which another function is integrated?
Nov
25
reviewed No Action Needed simplyfying boolean algebra
Nov
24
comment Why is integrability needed in fundamental principle 'you can't beat the system'?
For conditonal expectation to exist, do you not need the r.v. to be $L^1$? In this case, you need $C_n(X_n-X_{n-1})$ to be integrable. The easiest condition is to assume that both $C_n$ and $X_n-X_{n-1}$ are both $L^2$ and use Cauchy-Schwarz. Maybe you can try to construct counter examples where both are integrable but the products fail to be? Note Saz's answer assumed X.Y is integrable. If you can show the product is integrable than $L^1$ is okay but in many cases, it is easier to show $L^2$.
Nov
24
reviewed No Action Needed Proof that a certain language is Turing Decidable
Nov
23
awarded  Pundit
Nov
20
comment Find a graph where $|E| = 2|V|-3$ and $\deg (v) = 3$ for every $v$
That drastically changes the triviality of the problem...
Nov
20
comment Find a graph where $|E| = 2|V|-3$ and $\deg (v) = 3$ for every $v$
It did not occur to you to start with the graph with just 2 vertices and 1 edge? I fail to comprehend how you could have spent hours. What did you try?
Nov
20
reviewed Approve Find a graph where $|E| = 2|V|-3$ and $\deg (v) = 3$ for every $v$
Nov
20
comment Find a graph where $|E| = 2|V|-3$ and $\deg (v) = 3$ for every $v$
you certainly didn't try very hard.
Nov
18
comment Does $0$ correlation imply independence for marginally normal distributions?
@Henry How did you derive that?
Nov
14
accepted standardised random variable least square regression $X$ against $Y$, $Y$ against $X$
Nov
13
reviewed No Action Needed Quadratic equations in $\mathbb{C}$
Nov
12
comment increasing process
well, this follows from the Tanaka's formula (trivially), but I am guessing that is not the answer you are looking for. So maybe you want to look into a proof for Tanaka's formula.
Oct
24
comment 3 contestants choosing a smallest number to win a car
So this just seems like a 3 player prisoner dilemma problem. The only stable point is everyone chooses 1 and nobody win. If two player sample over 1 to N uniformly, i am going to pick 1 every time...
Oct
24
comment 3 contestants choosing a smallest number to win a car
If the players play this, one of the player should always choose 1 and have greater than 0.5 percent chance of winning
Oct
24
comment 3 contestants choosing a smallest number to win a car
I got the same numbers, so does this mean this game has no nash equilibrium?
Oct
24
comment 3 contestants choosing a smallest number to win a car
I am slightly confused. In prisoner's dilemma, both criminal should turn their friend in when they are not colluding. Your last sentence suggestions collusion? While this is in a way, optimal, it is certainly unstable.
Oct
24
comment 3 contestants choosing a smallest number to win a car
the optimal strategy cannot be over a large number surely? If 2 players do this, i can just choose 1 and 2 with probability 1/2 to beat this strategy. At the top, you said your assumption is the players are not cooperating, but settling for a distribution which make the prob of winning as close to 1/3 as possible is collusion.
Oct
24
comment 3 contestants choosing a smallest number to win a car
I don't quite know how to write down the max min (?) problem.
Oct
24
comment 3 contestants choosing a smallest number to win a car
@stochasticboy321 I am vaguely aware of the concept of nash equilibrium concept but I am not sure how we prove it in this case. in a perfectly rational world, the players would probably collude...