Recent content by crbazevedo

Well, let me roughly define what I mean by "separate": Without loss of generality, I say that two points x, y in R are "separated" if there exist 0 < epslon < ||x - y|| in R, so that the intersection between A = {x + epslon, x - epslon} and B = {y + epslon, y - epslon} is empty, where ||x -...

The existence of plateaus is something I had noticed empirically before. Your example confirms this, what is great, thanks. Now I'm wondering whether it is possible for a continuous joint CDF to have a discrete set of k separate maxima, say {(x1*,y1*), ..., (xk*,yk*)}, each of which yelding...

True or false: "Every joint CDF has only one global maximum at F(x1*, ..., xn*) = 1? I know that the multivariate CDF is monotonically non-decreasing in each of its variables. But does that imply that it has only one global maximum? Is it possible to have two or more separate peaks where the...

@bpet Yes, they are. So, what happens is that if one urn turns out to be full just after adding the j-th ball (j < m), that urn is simply removed and all the (j+1), ..., m-th balls need to be allocated to urns with available slots. But I'm not sure whether the order of placement will afect the...

Hi @bpet, thanks for the reply. Actually, the total capacity of all urns is simply the sum of their individual capacities, i.e., C(U_1, ..., U_m) = Sum_i=1^m C(U_i) = m + (m-1) + ... + 1 = m*(m + 1)/2. Thus, adding the (m+1)th ball would not be an issue. I'm generally interested in the specific...

Hi all, I'm working towards my Msc dissertation and I've ran into a tricky problem which I've figured it out to be modeled as the following urn problem: there are m balls and m urns U_1, ..., U_m with capacities C(U_1) = m, C(U_2) = m-1, ..., C(U_m) = 1. Knowing that each urn U_i is only...

Hello everyone, I'm new to this forum and I'm glad to have found such a high quality resource where we can have such valuable guidance and discussions. I've read somewhere that the variance of [tex]p(x) = {\frac{1}{n}}\sum_{i=1}^{n}\delta(x-x_i) \forall x \in \Re[\tex], in which [tex]D_n =...