Let 0<ε2<ε1<1. Consider a Monte-Carlo algorithm that gives the correct solution to a problem with probability at least 1-ε1,regardless of the input. How many independent e …

What are practical ways of doing so?

I'm trying to find the minimal (monic) polynomial $M(x)$ (over the rationals) for an algebraic number. I know the degree of the polynomial (call it $d$) and I have $d+1$ data point …

Suppose we have a Markov Random Field P(X1,...,Xn) on graph G. Suppose we know P(Xi,Xj) for every edge (i,j). Can we recover P(X1,...,Xn)? If G is a tree, then there's a formula f …

Inverse distance weighting is a common way of interpolating values zj at scattered data points Xj in Rn:     idw(P) = Σ wj zj / Σ wj   &n …

How do I test if the difference between probabilities is statistically significant. I know the population size and population variation. A simple t-test or ANOVA would work for var …

Is there an example of a differential operator $A(z)$ with parameter $z \in \mathbb{R}^d$ and Frechet derivative $A_z(z)$ such that $\mathrm{im}(A_z(z)) \subseteq \mathrm{ker}(A^T( …

I know from Maths at university that when you integrate you do that with respect to a variable Can you; 1) Integrate with respect to two variables at the same time? ie: integrat …

Hi, I'm working on regression models in STATISTICA application and I need to know what is Fisher-Snedecor distribution for and how to analyze my regression model in this distributi …

Let $(X,Y)$ be a random vector. Suppose that the marginal distribution functions of $X$ and $Y$ are known (say $F_1$ and $F_2$). Then the joint law of $(X,Y)$ is given by the follo …

Under what conditions on a and b is there a distribution $f_{a,b}$ such that the product $XY$ of two independent realizations $X$ and $Y$ from $f_{a,b}$ has a Beta(a,b) distributio …

I have a set of N bodies. The size of each body is being measured $m_i$ times ($m_i>1$ and different for each body). I would like to describe the resulting measurement. Particularl …

I'm looking for an overview of statistics suitable for the mathematically mature reader: someone familiar with measure theoretic probability at say Billingsley level, but almost co …

I have been working on a problem(alternate minimization) where I want to establish an inequality in which I am stuck. An $\alpha$- parameterized version of the divergence(Kullback …

Apologies if my question is poorly phrased. I'm a computer scientist trying to teach myself about generalized functions. (Simple explanations are preferred. -- Thanks.) One of the …