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...
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...
Homework Statement
Let Yi = (Z1 + ... + Zi)/(Z1 + ... + Zi+1) for i = 1,...,n and Yn+1 = Z1 + ... + Zn+1
where Zi ~ independent gamma(pi) for i = 1,...,n+1.
Prove that the Yi's are mutually statistically independent.Homework Equations
U ~ Dirichlet(p1,...,pn;pn+1) iff U = Z/T where Z is the...
Homework Statement
G is an abelian group with H the subgroup of elements of G with finite order. Prove that every non-identity element in G/H has infinite order. Homework Equations
The Attempt at a Solution
Suppose gH in G/H has order n.
Then (gH)n = gnH so gn is in H.
Then there is some m > 0...
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...