let $M_n$ = ($X_1$ + ... + $X_n$) / n and $\mu$ = E($X_i$), $\sigma$ = var($X_i$) Using Chebyshev's rule, we can prove that P( | $M_n$ - $\mu$ | >= $\epsilon$) <= $\sigma^2 / $ …

Suppose there is an oracle that returns a number $b \in \mathbb{Z}_{n}$ whenever I press the button. We have $b = a + e$, where $a \in \mathbb{Z}_n$ is a fixed number and $e$ is s …

Hi there im looking for a formula to decide if my sample size if good enough. My problem: I have population of 2 million items. I selected 50000 of them at random and I checked …

I believe that it is often the case that you are trying to select the best probability distribution to use to describe some phenomenon you are studying, and you have data not only …

I have a polynomial $p(x)=a_Nx^N+a_{N-1}x^{N-1}+\dots+a_0$. I want to convert this into another polynomial of same order, say $b_Ny^N+b_{N-1}y^{N-1}+\dots+b_0$. Is it possible to f …

I randomly sample uniformly from $ {1,..,N }$ without replacement until drawing a number $ \leq k$. Denote the expected number of draws by $R(N,k)$. I want a good approximation fo …

Hi, I need to generate a 'uniform sample' over an hemisphere and once done project it in a specific vector direction. I have try the following, but it produce some errors... mayb …

Sorry for the vague title but I couldn't find a better one. I want to compute the sum $S = \frac{1}{N}\sum_{i=1}^N c_i x_i$ where $c_i$s are known positive constants. The problem …

There are some pretty simple methods to do uniform sampling on the surface of high-dimensional spheres or cubes. Are there any methods that sample uniformly on the surface of a hig …

Let $B^{n} _p= ${$ (x_1, \dots, x_n) : |x_1|^p + \dots |x_n|^p = 1 $} be the unit ball in $\mathbb{R}^n$ in the $\ell^p$ norm. If $X_1,\dots,X_n$ are iid $\exp(1)$ -distributed ra …

Hi, So here is my problem: Given a nonlinear, discontinous, cost function $f(x_1,x_2,..,x_N)$ along with linear constraints $x_n \ge 0, \forall n$ $x_n \le c_n$ and $\sum_{n=1}^ …

The set of $n\times n$ real, nonnegative matrices whose rows and columns sum to one forms the well-known Birkhoff polytope Recently someone asked me if I knew How to sample (i …

I take a SRS sample of size n from a population of x values ranging from 1 to N. Each selected unit also has a probability p of success or q = 1-p of failure (i.e. the probability …

In one of my work I need to simulate random data from student's t copula using conditional sampling method. I know for elliptical class of copula method of simulation is different …

I have a binary space partitioning (BSP) tree which recursively partitions a hypercube using linear hyperplanes. That is, a hyperplane splits the hybercube in half, creating two co …