Recent content by hikaru1221

Woa this thread certainly gives me a fresh chill, visiting PF after so many years. Arguing that a mathematician is wrong (about life) could be pointless, unless it's about a step in their proof. What about those other than mathematicians? Who knows :rolleyes: But I tend to agree that the book...

You can try with \int sin^2(2t)dt - \int sin^2(2t)sin^2(t)dt, plus some trigonometric manipulations. P.S.: Silly me, perhaps you only need some trigonometric manipulations.

What we need to prove is P(w,x) = P(w)P(x). P(w,x) can be computed easily by integrating (or summing) P(w,x,y,z) over all y and z :wink:

I suppose the problem assumes A and B are statistically independent. Then the formal way to do this is: P(B>A) = \int_{b=-\infty}^{+\infty} \int_{a=-\infty}^{b}f_A(a)f_B(b)dadb This is a very nasty integral.

I think you're into too much math. The I(.) function, if I get its meaning correctly, is nothing but to indicate that it is impossible to sample x\leq\mu. With frequentists' approach, this means a lot: you can safely ignore the bunch of I(.)'s and consider only those samples greater than \mu...

I suppose that it is trivial to show X(t) and Y(t) are WSS :wink: So the problem is only to prove X(t) and Y(t) are jointly WSS. To do this, expand R_{XY}(t,t+\tau): X(t) = \int_{-\infty}^{+\infty}V(t-\alpha)h_1(\alpha)d\alpha Y(t+\tau) = \int_{-\infty}^{+\infty}W(t+\tau-\beta)h_2(\beta)d\beta...

hi, thanks a lot; that's very helpful :)

Hi, thanks for the reply :) So would it be better if I have an excellent LoR and so-so (or mediocre) LoR's than having all LoR's being good? It seems to me that it is hard to have all kinds of research experience in just a few years in undergrad while still being impressive - but this somehow...

Hello, I'm in my 3rd year now, and intend to do PhD after graduation (I major in Electrical Engineering, not Physics). As far as I've known, normally grad schools require around 3 letters of recommendation, so I think I really get to know well 3 professors. That's the problem: so far only one...

You can try with this: \frac{dy}{y^2} + \frac{dt}{t^2} = 0 :wink:

Yes, it is on average, no net flow, energy flow or mass flow. But I would doubt that it is about kinetic energy. The wall, unlike the ideal gas molecules, has potential energy - and it's definitely not negligible (think of the tight bond among the molecules). Some gas molecules may be held back...

Yes, equilibrium, that's a magic word. But sorry, no, you're still in the-ball-and-the-wall mindset, though it seems that you're heading the correct direction. You have to think of a bunch of balls, each with random behavior, heading to different positions on the wall, each position is rough...

Pardon me if I get things wrong. It's been such a long time that I haven't touched my physics. In my opinion, one of the most important observations that you've made is that if the temperature of the gas = temperature of the wall, then kinetic energy can be roughly conserved. Nice job! :wink...

For example, solving a traffic problem with a wave model. To me, creativity is more like you create something new / new perspective (in order to solve a problem), and the result is usually that it takes less time to solve it (and perhaps new insights). On the other hand, if the problem is solved...

Well that gives me a really hard time to find some examples, since I've been away from physics for so long; it seems like I don't really remember at all the problems I solved I have to look up for my past posts; you may want to look at this problem...