I'm working with four populations consisting of true/false events. They each have a different mean and variance. I have samples from each, with different sample sizes. Call the per …

I'm looking for a "nice" way to parametrize the joint distribution of multiple, possibly correlated discrete random variables on {0,1}. Even for N=2, there doesn't seem to be an ob …

This should probably be community wiki, but I don't know how to set that myself. I'm looking for examples or Markov chains that are used in statistics or statistical physics, and …

I'll explain the problem but what I am looking for is a few suggested methods to approach this problem. You don't need to know what a microarray but if you are interested look here …

Let $\mathbf X = [X_1, X_2, \ldots, X_n]^\mbox{T}$ be a vector random variable drawn from a known distribution with CDF $F(x)$. The CDF for the minimum value in $\mathbf X$ is cle …

In probability/statistics, there is a notion of two things being "independent", which would basically mean that any information we can get about one thing has no effect on our (pro …

I have a probability mass function of some experimental data who's log looks like the following: (please ignore the fact that it is not normalized) (meaning if p(x) is the pmf, t …

Dear Colleagues, This is a math question for people who know the rules of (American) football. Every year my barber runs a “football squares” game. He finds 100 customers, each p …

In Probability theory, does there exist some measures of peaked-ness for multi-modal distributions. I guess kurtosis as such would not be a good measure of peaked-ness for multimod …

Is there a univariate probability distribution $p_{\lambda,\alpha}(\beta)$ over the reals, parameterized by $\lambda > 0$ and $1 >= \alpha >= 0$, such that $p_{\lambda,\alpha} \pro …

First, the (simple!) setup: I have a Markov chain X t on some finite state space Ω with stationary distribution π, and a function f from Ω to R. I'd like to estim …

For a (possibly signed) nondegenerate probability measure $\pi$ on $\{1,\dots,n\}$ define $$\langle \pi \rangle := \{R \in \operatorname{STO}(n): \pi R = \pi \}.$$ Here $\operatorn …

I have a question for you and thank you in advance for your answers and ideas. Let us suppose that we have the marginal distributions of two r.v X and Y, and also the law of X-Y ( …

What is the explanation of the apparent randomness of high-level phenomena in nature? For example the distribution of females vs. males in a population (I am referring to randomnes …

I have two random variables X and Y. X follows a power law distribution. I know its generating function G(x). I also know the Pearson correlation coefficient of X and Y. How do I f …