Good day. I know getting the class interval given 3 as the highest value and 0.65 as the lowest value is easy. Here's the catch, the distribution of the interval starts at 1 which …

Consider a set of real numbers in $[a,b]$. I was wondering given their mean (no distribution), can we determine bounds on the median of these numbers? A wild guess would be the f …

Let $X_1, ..., X_n$ be i.i.d. sub-Gaussian random variables with mean $0$ and variance $1$. That is, we have $Pr[|X_i| > t] \leq \exp(1-t^2/K^2)$ for all $t>0$ and a parameter $K$. …

Assume the $1 \times N$ vector $\mathbf X = [X_1, X_2, \ldots , X_N]$ contains i.i.d. normal samples such that $\mathbf X$ has a multivariate normal distribution. Now assume anot …

I am a statistical physicist, and I've come across a problem that I don't know how to solve. I believe my issue lies with how to formulate it mathematically. I'd be very grateful f …

Prove the (numerically-evident) proposition that \begin{equation} \Sigma_{i=0}^\infty f(i) = 1, \end{equation} where \begin{equation} f(i)= 2^{-4 i-6} q(i) \frac{\Gamma(3 i+\frac{ …

suppose we have three variables here, x,y, z now, what we know is that the correlation between x and z is 0.6, the correlation between y and z is 0.65. Here is the question, is t …

I believe the following problem is related to something called the "voter model" in statistics. This is not my area of expertise so please forgive me if the answers turn out to be …

I am looking for a version of the Bayesian Linear Model in Banach spaces. Background: the finite dimensional case The following is a well-known theorem about normal correlation …

Hi, I have some repeated measures data, one measurement a day for three days in a row, and the measured variable looks normally distributed. I have two groups, the "really ill" and …

I am trying to make the most of computations that have already been performed in previous steps of an algorithm. Throughout this problem statement I am only mentioning correlation, …

What progress has been made towards sampling from the 2D lattice Ising model with the following Hamiltonian: $H=-J\sum_{\langle i,j \rangle}S_iS_j - \sum_i b_iS_i$ Where the firs …

Given a $N \times M$ matrix $X$ comprised of standard normal entries ($M > N$), I'm interested in approximating $E[trace((XX^T\frac{\gamma}{M} + I)^{-1}]$ in terms of $N, M$ and $\ …

Let $M$ be the real square matrix of a typed branching process, such that $M_{ij}$ is the expected value of offsprings of type $j$ emanating from type $i$. We know that if the fir …

Let me explain what I mean: The width of the average person varies, perhaps with a normal distribution. Given a specific variance, how many people (on average) can sit side-by-si …