5
votes
0answers
144 views

Generating a stochastic matrix with a given second dominant eigenvalue

I need a procedure (iterative or otherwise) that, given a positive integer $N$ and a (possibly complex) number $\lambda$ such that $0 < \vert \lambda \vert < 1$, will be able to generate an $N ...
0
votes
0answers
55 views

GA (Genetic Algorithm) and stochastic simulation to solve optimization in R

My problem is to solve the following optimisation problem using GA (Genetic Algorithm)and stochastic simulation. The goal is to solve the maximisation problem : \begin{equation*} \begin{aligned} ...
1
vote
0answers
162 views

Markov Chains - Using Gibbs & Metropolis algorithm.

Suppose $f_x,_y$ is bivariate normal distribution. I was given the parameters $(μ_1, μ_2, σ_1^2, σ_2^2)$ and $ρ=0.95$ the correlation coefficient. I want to generate $(x_1,y_1), ...
1
vote
4answers
285 views

Figuring out probabilities with Hidden Markov Models

I'm really new to Math so sorry in advance if this question does not make sense. Also I cross posted this on stats.stackexchange.com also. Background: I'm trying to learn about hidden Markov models ...
6
votes
2answers
479 views

Expected travel time for regularly departing trains

I'm going to ask a very simple practical question, but I believe it has some interesting mathematical properties. The simple variant is: trains depart every $x$ minutes and take $y$ minutes to arrive ...
5
votes
2answers
2k views

How do you check if a sequence of numbers is truly random? [duplicate]

Suppose a source produces an indefinite sequence of positive integers. How can you check whether the numbers are generated truly randomly?
3
votes
1answer
320 views

Analysis of a biased random walk related to median finding

Imagine a process with two variables min and max, and two counters hi and lo. We initialize min and max by selecting two random numbers (assume a uniform (0,1) distribution for convenience), and ...