# Tagged Questions

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### How to find out number of possible outcomes by trying over and over?

While working on my network exploration tool project, I've ran across the problem of reliably determining number of possible exit addresses of a tunnel with single entrance. I've came up with ...
71 views

### [Probability]need help to understand the following expression

So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively. assume c is a constant. I am having huge trouble to understand the integration of the following ...
31 views

### Select an element without uniform distribution with a uniform random without iterations

I have N elements (numbered from 0 to N-1) and I must choose one but without the same probability. For example, I need that the 0 must happen 50% of times, 1 with a 25%, 2 with a 12.5%, etc. I don't ...
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67 views

### How to construct a uniform joint distribution

I have a question that is critical to my work, but I am not sure if it is any possible. Assume that you have two uniform random variables X and Y. The product distribution of Z=XY is not a uniform. ...
137 views

### Finding functions where the increase over a random interval is Poisson distributed

I'm trying to construct a type of function $f(t_1, t_2)$ that counts the number of deterministically simulated Poisson events between two points in time. We can use a single valued function ...
284 views

### problem on random variable in probability

A game consists of first rolling an ordinary 6-sided die once and then tossing a fair coin once. The score, which consist of adding the number of spots showing on the die to the number of heads ...
406 views

### Random number generator with discrete probability distribution

Is there a general algorithm for implementing a PRNG with a probability distribution?
203 views

### Average number of bins occupied when throwing $n$ balls into $N$ bins

There are $n$ balls and $N$ bins. At each time, a ball is thrown in one bin of $N$ bins at random. This repeats n times. So that in total $n$ balls are thrown into bins. The question is, on average, ...
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### Chernoff type Sum of independent random variables having exponential tails

Say I have n independent variables $\{X_1,X_2 \dots X_n\}$ with Expectation 0 such that $Pr(|X_n| > \alpha) < e^{-\lambda \alpha}$. Can we produce chernoff type inequalities for the sum of these ...
47 views

### Property of a random distribution.

I have to get an integral in a previous post Help on an integral.. Some guru gave me hints of how to approximate its value, but I need approximation with largely varying $a$ and $b$. I realized that ...
188 views

### Fast generation of Pareto-distributed randoms.

I'm developing a library of routines for generating random numbers for simulations (it's on GitHub). I've included fast routines for normally distributed and exponentially distributed randoms, using ...
268 views

### Probability distribution of the product of two independent complex gaussian random variables

I have to calculate the pdf of $Z = X*Y$, where $X \in \mathcal{C}(\mu_x,\Sigma_x)$ and $Y \in \mathcal{C}(\mu_y,\Sigma_y)$, where $\mathcal{C}$ is a complex distribution. It can be assumed that ...
111 views

### Probability density function for the normalised sum of N random variables

I was wondering what the PDF looks like for Z= (1/N)*SUM(z_1+...+ z_n), where each z_i is computationally represented by RAND(). What is the behaviour of the PDF as N -> infinity?
119 views

### Generating a random number from a given distribution

I have a problem (a part of a Monte Carlo simulation) where I'm given the energy of an incoming particle, $\varepsilon$ and want to split this energy in two parts, randomly generating the fraction ...
115 views

### What is the distribution of $\min(r_1, r_2)$?

If I have 2 uniform random numbers $r_1$ and $r_2$ in $[0,1)$, what is the distribution of $\min(r_1, r_2)$? I have a problem I'm trying to get my arms around, and getting some context on this ...
394 views

### Generating random numbers with skewed distribution

I want to generate random numbers with skewed distribution. But I have only following information about distribution from the paper : skewed distribution where the value is 1 with probability 0.9 ...
154 views

### Random sampling from a conditional bivariate normal distribution

How does one draw a random sample $\begin{bmatrix} X_i \\ Y_i\end{bmatrix}$, $i=1,\ldots,n$ from the conditional distribution of a bivariate normal distribution, given specified values of the the ...
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### What discrete distribution is completely determined by its mode and variance, is easy to sample, and has nice border properties?

I need to generate random ordered unranked trees that will be used to test some computer program. I'd like to incorporate some kind of control into the generation process, so that the generated trees ...
284 views

### Repeatedly Toss Balls into Bins

$n$ balls are randomly tossed into $m$ bins, each bin can hold $k$ balls. If a ball is tossed into a full bin (already has $k$ balls in it), it can be tossed repeatedly and randomly into the $m$ bins ...
67 views

### Finding a distribution for random number generation

I am writing a program for solving the shortest path in travelling salesman problem, with a twist that there are multiple salesmen who partition the cities among themselves, thus creating two part ...
215 views

### How to deal with non random data in statistical analysis?

I have a set of monthly water quality data, and I want to use them in a few statistical analysis (such as finding distribution or using in copula models) which require random variables as input. I ...
1k views

### Cumulative distribution function determine the random variable

I don't know that determine is the right word, but I try to explain. What I need to understand. :) So.. We know's that if a function fit this conditions: Monotonically non-decreasing for each of its ...
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### Off-lattice Brownian bridges in R^3

Start at a point $(0,0,z_0)$ and take $n$ steps of unit length in a random direction (for each step) in $\mathbb{R}^3$. Let such a walk be valid if the position of the last step, and only the last ...
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### Repeating something with (1/n)th chance of success n times

Is there anything that can be said about how many attempts it will take to correctly guess a random number out of 1000 numbers? If the number wouldn't change the probability would just increase every ...
289 views

### CDF of standard normal random variable never actually is 0 or 1, right?

The CDF of a standard normal random variable is never actually 0 or 1, they only approach 0 and 1, correct?
502 views

### Trends in the distribution of reordered digits of Pi (OEIS A096566)

First let me try to describe in more details below the approach of "reordering" digits of Pi, which is used in OEIS A096566 https://oeis.org/A096566 and what I have done analyzing it so far. I am ...
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### Are my steps to generate random values based on a given dataset correct?

I have a dataset of 100 cases. Each case has a class {I,II,III,IV,V} and a value A and V, each class appears exactly 20 times in the dataset: ...
654 views

### A problem on random variable in probability

I am a starter in maths. I am doing pretty good in all other topics except for probability. I don't know why I am always confused in it. My exams are nearby and I still cant solve simple problems. Can ...
124 views

### Inner product of two vectors with Rademacher random entries

I am lost with the signs cancellation. Please help me to calculate this inner pruduct. Let $a$ and $b$ be two $2m$ dimentional vectors such that their entries are Rademacher random variables and ...
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### Selecting numbers on a number line where distribution tends to cluster at one end.

Lets say I've got a number line from $1$ to $100$. I want to randomly select $20$ integer numbers from the number line. But I want the numbers to tend to come from say $1$-$50$, with only a few coming ...
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### what should be the frequency distribution of the eigenvalues of a randomly generated hermitian matrix?

I'm getting the eigenvalues of a randomly generated hermitian matrix distributed like a normal probabilistic distribution(crowded in the middle values ) but my sir told me that it should be a ...
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### Generate random numbers that are sums of hidden variables

I have $Y = A X$ where: $Y$ is an $m$ vector of random variables $X$ is an $n$ vector of random variables, uniformly distributed in $[0, 1]$ $m \ll n$, ($n$ ~ $m!$) $A$ is an $m \times n$ $0/1$ ...
I have two i.i.d. random variables $X$ and $Y$ and I want to generate a set of $n$ random samples from the distribution of the ratio between the two variables $Z=X/Y$. The pdf of $Z$ is described by: ...