Recent content by iomtt6076

Where does that number come from and what are the units? I ask because I thought the charge of an electron is -1.602 x 10^-19 Coulombs. An alpha particle is two protons and two neutrons. Only the protons have charge so...

Actually... it does: I = 2\pi\int_0^\infty\,dR\int_0^\pi\sin\theta e^{irR\cos\theta}\,d\theta =2\pi\int_0^\infty\,dR\int_0^\pi (-\frac{1}{irR})\,de^{irR\cos\theta} =\frac{4\pi}{r}\int_0^\infty\,dR\frac{1}{R}\frac{e^{irR}-e^{-irR}}{2i}=\frac{4\pi}{r}\int_0^\infty\frac{\sin...

Homework Statement Problem 8.30 from Greenberg's Foundations of Applied Mathematics: We meet the integral I = -\frac{1}{8\pi^3}\int_{-\infty}^\infty\int_{-\infty}^\infty\int_{-\infty}^\infty\frac{e^{i(\xi x+\eta y+\zeta z)}}{\xi^2+\eta^2+\zeta^2}\,d\xi\,d\eta\,d\zeta when we solve the...

Okay, I see what you're saying; I agree it should be \frac{1}{t}\int_0^t x^2(\tau)\,d\tau Thanks, I got it now.

Thank you for the reply. Yes, I've now found out that E = (1/2)m\omega^2 A^2. Well, I've copied it exactly the way it shows up on the problem set, so maybe the professor made a typo?

Homework Statement For a given total energy E0 compute and compare a time average and a phase space average of x2 for the harmonic oscillator. The one-dimensional Hamiltonian is H = \frac{p^2}{2m}+\frac{m\omega^2}{2}x^2 Reminder: the time average is defined as \langle x^2\rangle...

Motorcycle racing fans on PF - fantastic! Can't way for the 2010 seasons to get underway. Anyway, as far as recent battles go, I thought Spies vs. Haga @ Assen was ace: http://www.youtube.com/watch?v=GBgRKPcscco"

Apologies for the (very) late response. When you write P(X=n) = (0.001^n)(e^-0.001)/(n!), you are saying that the Poisson parameter is .001, which is not true. In this problem, the Poisson parameter is supposed to be approximated by np, as mentioned above. The value .001 is used for...

I don't think you have to worry about expected values here. When you model the number of errors with a binomial distribution, you want to find the probability of 0 "successes." "Success" in this case means a character being corrupted, which happens with probability .001. So you want to find...

Thanks to both of you for your help; I finally got it. I found that drawing a picture by taking slices through the U2-axis was also essential.

Why isn't it \int_0^1\int_0^1\int_{2\sqrt{U_1U_3}}^1 dU_2\,dU_1\,dU_3 I can't figure out why my limits of integration for U2 are wrong.

Are we trying to find the volume above the surface defined by U_2=2\sqrt{U_1U_3} and inside [0,1]x[0,1]x[0,1]?

Homework Statement Let U1, U2, and U3 be independent random variables uniform on [0,1]. Find the probability that the roots of the quadratic U1x2+U2x+U3 are real. Homework Equations The Attempt at a Solution So we need to find P(U22>4U1U3), which involves evaluating some...

I think it comes from the hypothesis of nested intervals. If there exists an m such that bm is not an upper bound, then ak>bm for some k. So [ak,bk] would be disjoint from [am,bm], which contradicts the assumption of nested intervals. When you have a sequence of nested intervals, no two...

Definition: A number s is the supremum for a sequence if : 1) s is an upper bound for the sequence 2) if p is any upper bound for the sequence, s is less than or equal to p so we are talking about 2) here. bm is an upper bound for the sequence; thus by definition sup an<=bm. It doesn't matter...