Approximation Definition and 768 Threads

For a binomial distribution with n=10 and p=0.5 ,we should not use the poisson approximation because both of the conditions n>=100 and np<=10 are not satisfied. SUppose we go way out on a limb and use the Poisson aproximation anyway. Are the resulting probabilities unacceptable...

i'm stuck trying to figure out this probabilities problem for my thermodynamics class. the question is: consider an idealized drunk, restricted to walk in one dimension (eg. back and forward only). the drunk takes a step every second, and each pace is the same length. let us observe the...

It seems to me that I've got part (a) right, but I'm not so sure about what I have in part (b). I just need to know whether or not I am on the right direction. Any help is highly appreciated. :smile: Problem The force due to gravity on an object with mass m at a height h above the surface...

Hi, I'm trying to evaluate the following integral to calculate the scattering cross section for a spherically symmetrical potential e^{\frac{-r^2}{a^2}}? f(\theta)=\int r e^{\frac{-r^2}{a^2}} sin(kr) dr where a is a constant. What is the easiest way to evaluate this? I was able to get...

I'm using the laplace approximation (also known as MacKay's evidence framework) to the posterior volume of a baysian model. The standard procedure is as follows: 1) Find the (local) maximum point of the posterior pdf i.e optimise the parameter values. 2) Evaluate the hessian matrix(H) by a...

Derive \frac{n_1}{s_o} + \frac{n_2}{s_i} = \frac{n_2-n_1}{R} for Gaussian optics from the following equation \frac{n_1}{l_o} + \frac{n_2}{l_i} = \frac{1}{R} \left( \frac{n_2s_i}{l_i} - \frac{n_1 s_o}{l_o} \right) by approximating l_o = \sqrt{R^2 + \left( s_o + R \right) ^2 -...

I need to find thelocal approximation of f(x)=x^(1/3) at x=26.6, knowing f(27)=3. Here's what I did, don't know if I did it right: f '(x)=(1/3)x^(-2/3)=[x^(-2/3)]/3 slope of the tanget = slope of the secant [x^(-2/3)]/3=(y-y1)/(x-x1) [26.6^(-2/3)]/3=(y-3)/(x-27) now I sub in X and...

For a simple damped oscillator... \text {Apparently if } \beta \ll \omega_0 } \text { then ...} \omega_d \approx \omega_0[1-\frac {1}{2}(\beta/\omega_0)^2]} Given that: \beta=R_m/2m \text { (where } R_m= \text {mechanical resistance) } \text { and } \omega _d=\sqrt{(\omega...

when: g'(2)=1 g'(3)= -2 msec=mtan g'(2.5)=(y2-y1)/(x2-x1) =(-2-1)/(3-2) =-3/1 =-3 I got this question wrong on a test, were was my mistake?

How do I find integrals like \int_{a}^{b} \left( x^2 + 1 \right)^2 \ dx . This one is easy, since I can just turn it into \int_{a}^{b} \left( x^4 + 2x^2 + 1 \right) \ dx . But what if it would say \int_{a}^{b} \left( x^2 + 1 \right)^{40} \ dx ? What technique should I use?

Is there any way to tell in general if an integral in the form of \int x^n*e^{x^m} dx where n and m are constants is solvable without approximation?

Can anybody explain to me what the Born approximation is?

Hello there. I'm currently dead beat on this problem, maybe because I'm not sure I quite understand what it's asking (I'm taking my upper level mechanics course in germany, and I don't have any books, and it's the second week, and I'm up at 4am with 2 problem sets due tomorrow, each half done...

I am a bit confused about taylor approximation. Taylor around x_0 yields f(x) = f(x_0) + f'(x_0)(x-x_0) + O(x^2) which is the tangent of f in x_0, where f'(x) = f'(x_0) + f''(x_0)(x-x_0) + O(x^2) which adds up to f(x) &=& f(x_0) + (f'(x_0) + f''(x_0)(x-x_0) +...

I'm doing a problem on Van-der Walls interaction and was told in the hint of the problem to use the approximation kT>>hw to simplify {-hw/(2kT)}-Ln[Exp[-hw/(kT)]-1] I have no idea how to apply this approximation to simpify the problem. Thanks

Does anyone know the basics of the local spin density approximation?

http://www.geocities.com/dr_physica/moa.zip is a delphi program showing how my method of approxim outperforms/beats the Newton's one while looking for sqrt(2) try the case A+B=2*sqrt(2) and see the magic!

I was wondering how Stirling's approximation x! ~ sqrt(2[pi]x)xxe-x was derived. Anyone know?