# Tagged Questions

44 views

### binomial coefficient: maximum value

For $n\rightarrow \infty$ we consider $$f(p)=\sum_{j=c}^n {n\choose j} p^j (1-p)^{n-j}.$$ We are interested in $\hat{p}:=\arg \max_p f(p)$. Can we say something about $\hat{p}$ dependent on $n$ and ...
23 views

### monotonicity of binomial coefficient

I am interested in $$f(x):={k-1 \choose x-1} p^{x} (1-p)^{k-x}.$$ How do I find out in which Domain this function is monotonically increasing, in which it is monotonically decreasing? For which $x$ ...
55 views

Let $\phi \in \mathcal ( [0,1]^2)$ symetric , can we find a solution to the following minimisation problem? $$\inf \left\{ F[\nu] : \nu \in L^2 , \nu \geq 0, \int _0 ^1 \nu=1\right\}$$ with $$... 1answer 56 views ### Which Queue to Join at the Super Market Last night I started wonder about the fastest way to take a shopping trip with my university flat mates and was wonder about how we should queue for the check out. I have a feeling that queue theory ... 0answers 17 views ### Decreasing step size in SA algorithms I don't understand why deceasing step sizes implies "implicit" averaging of the noise in stochastic approximation algorithms 0answers 88 views ### Calculating the maximum of a function How can one determine$$\max_{f_0,f_1}\frac{\int_{\mathbb{R}}f_1(y)^xf_0(y)^{1-x}\log\left(\frac{f_1(y)}{f_0(y)}\right)\mbox{d}y}{\int_{\mathbb{R}}f_1(y)^xf_0(y)^{1-x}\mbox{d}y}$$given ... 2answers 105 views ### Estimating the maximum of a Brownian motion over the unit interval Let \left(B_t\right)_{t \in \left[0,\infty\right)} be a standard Brownian motion over the probability space \left(\Omega, \mathcal{A}, P\right). For each x \in \left(0, \infty\right), give an ... 0answers 20 views ### Randomized optimization: confidence bounds I am not sure whether the question is appropriate for MSE, so please feel free advise another website in the network. Suppose I have a Lipschitz continuous function f:X\to \Bbb R where X is a ... 1answer 73 views ### Bounded logarithmic function I am trying to find any function that it grows logarithmically up to a certain point, and after that point it remains constant. Can anyone help me with that 1answer 39 views ### Theory of Moments: Notation I try to read some papers about Moment Matrices/Optimization over polynomials, but I have some troubles with the following notation: Let P(V) be a power set of some V=\{1,2,...,n\}, how does a ... 0answers 79 views ### Learn about reproducing kernel Hilbert spaces? Why are reproducing kernel Hilbert spaces an important topic to learn? What is possibly achievable with that theory that is not reachable with just standard Hilbert space theory? 1answer 146 views ### Goofy problem: Optimal bet with nearly no knowledge A year or so back, on the verge of falling asleep, I thought up this question: You have come to me ready to gamble. I have two envelopes on the table, one containing the amount of my bet, and one ... 0answers 115 views ### Relation between maximizer's derivative and maximizing function Let u(x) be a continous bounded function such that u'(x) >0, u''(x) < 0. Define A(x) = -\frac{u''(x)}{u'(x)}>0. Let Y be a random variable with \mathbb{E}|Y|<\infty. I solve a ... 0answers 41 views ### How to go about optimizing this function? (Maximizing) If we are given a fixed integer N > 0 of choices we can pick out of a pool of k values c_0, \cdots, c_k (with repetitions allowed and c_i > 0 \forall i) and we want to maximize the ... 0answers 89 views ### Existence of a general-purpose (almost) universal optimization strategy From Wikipedia about interpretations of no free lunch theorem A conventional, but not entirely accurate, interpretation of the NFL results is that "a general-purpose universal optimization ... 1answer 298 views ### Understanding no free lunch theorem From Wikipedia: Y^X is the set of all objective functions f:X→Y, where X is a finite solution space and Y is a finite poset. The set of all permutations of X is J. A random ... 1answer 115 views ### Suitable Loss function for Order preserving Factoring of a matrix? (Old-Question) Given a n\times n symmetric matrix X, I would like to factor it using a vector c of size n \times 1 such that: \sum_{i,j} [X_{ij} \cdot c_i\cdot c_j] is minimum. How can I ... 2answers 1k views ### One vs multiple servers - problem Consider the following problem: We have a simple queueing system with \lambda% - probabilistic intensity of queries per some predefined time interval. Now, we can arrange the system as a single ... 1answer 97 views ### What is the maximum value of the minimum number of balls per bin? S people, N bins, each person has a given subset of bins he can cover, each person is given t balls. Question: What is the maximum value of the minimum number of balls per bin? i.e., allocate ... 1answer 100 views ### An optimal regression problem/proof I want to find a function f that given x will predict y. The expected prediction error of f is$$e = E[(Y-f(X))^2]=\int \int [y-f(x)]^2 p(x,y) dx dy the expectation of $(Y-f(X))^2$ with ...
Given a collection of points $P \subset \mathbb R^3$, a crude characterization of the "shape" of $P$ is sometimes given by the principal components. We construct a covariance matrix, e.g., if $P$ is ...