Recent content by oleador

I think we can apply the Central Limit Theorem here (correct me if I'm wrong). The number of observations should be large enough to use the CLT -- the death rate was measured weekly for several years. Then by the CLT the distribution of weekly death rates should converge to the normal...

The set notation is used ...everywhere. Open any more or less advanced math book (university level), and you will find this notation. A lot of mathematical results involve sets of numbers, functions, etc. The field that studies the properties of set is called Set Theory, and those properties...

Your intuition is correct. More precisely, x is a variable, and the set is a collection of all x's that satisfy the property specified in the definition of the set.

The notation {x | property of x} reads: the set of all x which have the stated property of x. From what I've read, it seems you understand what the notation means -- it is really that simple :) Correction: it should be "less than 16" in your definition of the set.

The Euler's proof is just beautiful! Proofs like these make me love mathematics.

Look for the Riemann zeta function. en.wikipedia.org/wiki/Riemann_zeta_function

A,B,D look correct. C. it is the geometric distribution. To find P(y>=200), you have to find 1 - F(199), where F is the cdf of the geometric distribution.

I am also interested in the question, but the answer is not clear to me. So, is it correct that the quantifier "for all but finitely many" may relate to either finite or infinite amount of elements depending on whether the set of the elements is a finite or an infinite set? If so, does this...

Ok, perhaps I misread your proof.

Sorry, that's a typo. Obviously, I meant "dependent". Edited the post.

The intuition for why you have to multiply the combinations is that for every possible combination, say, in [1,18] you can have 18C2 of combinations in [19,36] and 19C2 in [37,55].

Think about this as follows: how many ways are there to choose 2 numbers from 18? (no replacement, order doesn't matter)

@ chiro: Note that in general: E(X^2)≠(E(X))^2 @ zzzhhh: The proof is a simple application of the definition of covariance and the properties of independent random variables. The question should be in the Homework forum. Proof: Cov(A,B)≠0 \Rightarrow A and B are dependent, so prove that in...

I know Matlab is quite different from Fortran, but maybe this will help: http://www.mathworks.com/matlabcentral/fileexchange/28889-kronecker-product/content/kron.m

True. Confused \forallε>0[x≤y+ε]\Rightarrow x≤y with \forallε>0[x≤y+ε\Rightarrow x≤y]. The former is true. This, however, does not change my conclusion. ε=2(x−y) doesn't work, while ε=(x−y)/2 does.