Tagged Questions

0
votes
0answers
20 views

how to get the class interval given the distribution starts at 1, 3 as the highest value and 0.65 as the lowest? [closed]

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 …
0
votes
0answers
25 views

Bounds for the median of a set of value bound numbers, given their mean. [closed]

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 …
2
votes
0answers
204 views

Concentration of sum of independent random variables

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 $K$. …
0
votes
3answers
174 views

Probability that one RV will exceed many others

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 …
3
votes
2answers
151 views

Probability distribution for two-state system that depends on residence time

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 …
0
votes
0answers
218 views

Prove that the sum of a certain infinite series is 1

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{ …
2
votes
1answer
88 views

correlation for three variables? [closed]

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 …
1
vote
1answer
102 views

Transition time in finite voter model

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 …
0
votes
0answers
48 views

Normal correlation theorem in Banach spaces

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 …
1
vote
1answer
24 views

ROC curve with repeated measures

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 …
1
vote
0answers
46 views

Placing Bounds on Correlation/Covariance Through Correlation with an Intermediate Variable

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, …
3
votes
1answer
112 views

Exact sampling from 2D Ising model where coupling is constant?

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 …
2
votes
1answer
88 views

Expectation of the trace of an inverse of a random matrix

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 $\ …
2
votes
1answer
66 views

The first eigenvalue of a branching process matrix

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 …
3
votes
1answer
349 views

The average number of people that can sit on a bench of a given length.

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 …

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