Recent content by euroazn

this is what I figured and of course it's easy to see that the auxiliary equation has a lot to do with expectations, but confidence intervals aren't quite so easy :( Thanks for your help, you've been very useful!

You are vastly overthinking this. Consider the following problem: we have 3 red balls, 3 blue balls, and a green ball. How many different ways can we allocate them between 3 buckets?

There's a bunch of literature out there about empirical/data-fitting/statistical concerns regarding autoregressive times-series models, but is there anything out there about theoretical implications of a time-series being autoregressive? For example, when does limt → ∞E(Xt) exist? Does the...

Let's factor 3000 into primes. We are left with 23*3*53. Now we are left with a very simple combinatorics question. Can you figure it out? Think about what items you are selecting and what you are placing them into.

Yes, this is perfect. I think ARMA is exactly what I'm looking for. Thanks a bundle!

Oh, I am well aware that it doesn't DEFINE a stochastic process, but if it were to satisfy these conditions, do we know anything nifty about the process? Edit: The random X's form a time series if that's not clear.

Is it markov if we consider states to be vectors of the past n states?

E(Xn+1+i)=Ʃn+ij=i+1 cj-iXj, where Ʃnj=1 cj = 1. n is a fixed constant here, c is a fixed set of n coefficients. Can anyone tell me anything about such a process?

Thank you! Now that I at least know the name of this type of equation I can probably figure out the solutions given a restricted set of c(t) myself. EDIT: Or maybe not... it seems that constants for c(t) are about as good as it gets...

I was busy doodling and basically ended up constructing this differential equation: p'(t)=c(t)p(t)-c(t-T)p(t-T) Obviously I've dealt with eq's like p'(t)=c(t)p(t) but I'm getting stuck because of the second term. Does this differential equation even have a closed form? Thanks.

Wow! Only one hour! Impressive ~ And the solution is accurate too (conservation of momentum) My first post was just a "test" question, so to speak (I wouldn't be trying for Physics Olympiad if I didn't know about conservation of momentum =P) and I'm really impressed with the speed. More...

Hi, I'm practicing for the physics olympiad qualifier and I came across this problem: A spaceborne energy storage device consists of two equal masses connected by a tether and rotating about their center of mass. Additional energy is stored by reeling in the tether; no external forces are...