# Questions tagged [simulation]

A vast area which includes generating results from computer models.

27 questions
950 views

### What are numerical methods of evaluating $P(1 < Z \leq 2)$ for standard normal Z? [closed]

Let $Z \sim Norm(0, 1)$ and denote its PDF and CDF by $\phi$ and $\Phi$ respectively. Then, theoretically, $P(1 < Z \leq 2) = \Phi(2) - \Phi(1).$ However $\Phi$ cannot be expressed in closed form, ...
53k views

### Generate Correlated Normal Random Variables

I know that for the $2$-dimensional case: given a correlation $\rho$ you can generate the first and second values, $X_1$ and $X_2$, from the standard normal distribution. Then from there make $X_3$ ...
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### Why is this coin-flipping probability problem unsolved?

You play a game flipping a fair coin. You may stop after any trial, at which point you are paid in dollars the percentage of heads flipped. So if on the first trial you flip a head, you should stop ...
3k views

### What is the optimal path between $2$ fixed points around an invisible obstructing wall?

Every day you walk from point A to point B, which are $3$ miles apart. There is a $50$% chance each walk that there is an invisible wall somewhere strictly between the two points (never at A or B). ...
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### Probability that a quadratic equation with random coefficients has real roots

Consider quadratic equations $Ax^2 + Bx + C = 0,$ in which $A, B,$ and $C$ are independently distributed $Unif(0,1).$ What is the probability that roots of such an equation are real? This problem is ...
3k views

### Simulating uniformly on $S^1=\{x \in \mathbb{R}^n \mid \|x\|_1=1\}$

A scheme to generate random variates distributed uniformly in $S^2=\{x\in \mathbb{R}^n \mid \|x\|_2=1\}$ is well known: generate a standard normal variate in $\mathbb{R}^n$ and normalize it to unit ...
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### Implementing Ornstein–Uhlenbeck in Matlab

I am reading this article on Wikipedia, where three sample paths of different OU-processes are plotted. I would like to do the same to learn how this works, but I face troubles implementing it in ...
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### Why is a simulation of a probability experiment off by a factor of 10?

From a university homework assignment: There are $8$ numbered cells and $12$ indistinct balls. All $12$ balls are randomly divided between all of the $8$ cells. What is the probability that there is ...
551 views

### Computational methods for the limiting distribution of a finite ergodic Markov chain

We wish to show what can be discovered about the limit of a finite, homogeneous, ergodic Markov Chain $X_1, X_2, \dots,$ using simple methods of computation and simulation. Specifically, consider the ...
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### Managing a bond fund: Simulating the maximum of correlated normal variates

Two rating agencies score the safety of bonds in a particular population on separate standard normal scales. Because the two agencies take some of the same factors into account in their ratings, the ...
195 views

### Simulate simple non-homogeneous Poisson proces

Consider a Poisson process whose conditional intensity is $$\lambda(t) = \alpha e^{-t}$$ starting at time $t=0$ for some parameter $\alpha>0$. I would like to simulate arrival/event/failure ...
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### Monte-Carlo simulation with sampling from uniform distribution

I used to work with Monte-Carlo simulations for a while. In my case, I generated random data for a variety of input parameters according to uniform distributions (with non-negative support), say for ...
662 views

### Drunkards walk on a sphere.

I simulated the following situation on my pc. Two persons A and B are initially at opposite ends of a sphere of radius r. Both being drunk, can take exactly a step of 1 unit(you can define the unit, i ...
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### Numerical approximation of Levy Flight

I'm trying to produce a computer simulation of a Levy Flight in 2-dimensions; an approximation would be ok. Please excuse the simplistic level of this question: my maths is very rusty. My proposed ...
170 views