Recent content by SpringPhysics

Sorry for double-posting. The problem has been solved.

Homework Statement I wish to determine whether a SINGLE instrument provides reliable measures (test-retest reliability). This single instrument is not random (it's the only one available), and I will take 10 measurements for each individual that is part of a control group (and then again for...

UPDATE: I solved the problem using exponentials (a bit tedious but it worked). This thread can be closed now.

Homework Statement Show that the sample acf at lag h for n observations of xt = cos(wt) converges to cos(wh) as n tends to infinity. Homework Equations The sample acf at lag h is defined as the sample autocovariance function at lag h divided by the sample autocovariance function at lag 0...

haruspex: Yes, I've already figured out the relative probabilities. I don't see how this is a sum of a geometric series though. Do you mean to simplify as exp(Ʃ[Xi * (log(a1) - log(a2)) - (a1 - a2)]} where the sum goes from i = 1 to N I still don't recognize the distribution. EDIT: I...

Homework Statement I am trying to determine the posterior distribution of N where given a sequence of n independence Poisson random variables, the first N come from Poisson(a1) and the next N+1st to the nth ones come from Poisson(a2). The prior distribution on N is discrete uniform on the...

So that's basically what I said in my previous post, right?

So by definition of a limit, lim n→∞ xn = xn+1 which means that the sequence converges to some limit L. From here: - I can use either that any convergent sequence in ℝn must be Cauchy - or that the above implies that there is some N, M (natural numbers) such that || xn - L || < ε/2...

I don't see how to show that the series converges if I am only given that the sum is finite. All I get from subtracting partial sums is that the norm of the difference is yet again finite...

Homework Statement If a sequence {xn} in ℝn satisfies that sum || xn - xn+1 || for n ≥ 1 is less than infinity, then show that the sequence is Cauchy. Homework Equations The triangle inequality? The Attempt at a Solution || xm - xn || ≤ || Ʃ (xi+1 - xi) from i=n to m-1|| Using...

Wouldn't we be assuming that f and g are invertible? Or does that have no bearing on the proof? (I always got stuck because I thought we couldn't apply f or g inverse since we would have to then assume that f and g are invertible functions.)

Homework Statement Let X and Y be independent random variables. Prove that g(X) and h(Y) are also independent where g and h are functions. Homework Equations I did some research and somehow stumbled upon how E(XY) = E(X)E(Y) is important in the proof. f(x,y) = f(x)f(y) F(x,y) =...

I solved the tedious resulting system of equations and got 3=2...which means that there is no such rotation? EDIT: I get the angle of rotation as 0 when solving for the coefficient of xy to be 0, but according to the formula from the link, the angle should be pi/8. EDIT2: I get -pi/8 for the...

Homework Statement Determine the integral of f(x,y)=xy over x^2 - xy + 2y^2 = 1 in terms of an integral over the unit circle. Homework Equations The Attempt at a Solution The associated hint is to complete the square (which I did...and got messy expressions for x and y). I would...

Oh wow, I feel so stupid. I forgot that I was differentiating at 0, so I had point a = (x,y) and I was stressing out about why the limit wouldn't go to 0. LOL. Thank you greatly for your help and patience!