Given a covariance matrix, how can I construct a vector of expressions of randomly distributed variables whose covariance matrix is equal to the given one? I have an algorithm tha …

Why is Beta(1,1) the maximum entropy distribution over the bias of a coin expressed as a probability given that: If we express the bias as odds (which is over the support $[0, \i …

I hope this is an appropriate forum for this question, and I asked on math.stackexchange as well. If it doesn't belong, I don't mind closing this. If my questions is not clear, p …

ERNIE is a hardware random number generator used to generate winning Premium Bond numbers in the UK. Wikipedia says: "ERNIE's output is independently tested each month by an indepe …

When does the following hold? $\sum_{(i_1,\ldots,i_k)\in E} \frac{n!}{i_1! \ldots i_k!} \le \exp(n H^*)$ Where $H^*=\max_{(i_1,\ldots,i_k)\in E} -(\frac{i_1}{n}\log \frac{i_1}{ …

Most methods (that I know of) of numerically approximating the solution of ODEs are "general linear methods". For this type of method, the so-called 'linear stability' is examined …

Hi, I am doing some Kernel density estimation, with a weighted points set (ie., each sample has a weight which is not necessary one), in N dimensions. Also, these samples are just …

Suppose I have N real random variables with identical PDF. At every instance of these r.vs, I pick $K$ largest out of $N$. Lets call their sum as $S_K$. Alternatively, based on …

We define a process $\chi_k^n=\sum _{i=1}^k x_i^n$ where x_i are iid gaussian processes. I try to find the distribution of $\chi_k^n$. If k=1 then we get $f(x^n=y)=\frac1n y^{\fra …

Is it possible to use Fisher Information at p to get a useful upper bound on KL(q,p)? KL(q,p) is known as Kullback-Liebler divergence and is defined for discrete distributions ove …

Suppose we have a vector of probabilities $\mathbf{p}=(p_1,...,p_n)$, where $p_i>0$ for $i=1,...n$ and $\sum p_i=1$. Define new vector $\mathbf{r}=(r_1,...,r_{n-1})$ in a followin …

In Freedman's series of 3 books on Markov processes, I find that I keep on running into terms like: P[$\max_{0 \leq s \leq 1, s \leq t \leq rs}$ | B(t) - B(s) | > $\epsilon$] in …

Suppose there are two correlated random variables $X_1$ and $X_2$ both are gamma distributed but having different shape and scale parameters with correlation coefficient $\rho$. Wh …

Let $\xi_t$ be a zero-mean gaussian process on $[0,1]$ with covariance operator $C$. I would like to better understand the relation between the covariance operator and the regular …

http://mathoverflow.net/questions/21347/estimating-the-mean-of-a-truncated-gaussian-curve assumes that we know how many of the non-positive values are observable. How can this be e …