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Questions tagged [random]

Questions relating to (pseudo)randomness, random oracles, and stochastic processes.

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1answer
11 views

Joint probability distribution function and expected value

Lets say for we have a first dice and a second dice, with X representing the face of the first dice and Y representing the face of the second dice. I know that E(X) = E(Y) = 3.5 $$ E(XY) = \sum_{(x,y)...
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1answer
36 views

Billiards in a holey square

Suppose you start a point-billiard (or light ray) in a square at a random location, shooting off at a random angle, reflecting with angle-of-incidence equals angle-of-reflection. In general, because ...
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26 views

simulation/ probabilty

Suppose a population control plan for the country of Transylvania allows parents to have at most four children each, and they must stop having children when they get two girls. Explain how to ...
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15 views

Number of distinct sites visited by a random walk in one dimension

Is there a paper which explains how the number of sites visited by random walkers on a one dimensional lattice evolves depending of the number of steps ? I'm looking for a way to demonstrate that for ...
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0answers
18 views

(Non-replacement deck draw)Adding together increasing probability of drawing target card?

This is more a question to explain if there is any value in simply adding the probability of each subsequent draw from a deck to get a target card? What I mean is: 1/52 + 1/51 + 1/50 + 1/49 .... ...
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15 views

Taking SRS of a non normal/normal distribution

I was studying how taking Simple Random Samples of a non-normal distribution change the shape of the distribution. But how do I exactly take an SRS of a distribution? For example, consider a normal ...
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0answers
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Covariance matrix under multiplication with independent random variable.

assume two dependent random variables X and Y with their covariance matrix $\Sigma_{ij}$. Now assume one multiplies X with another independent random variable Z. The variance of the resulting random ...
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0answers
11 views

Generating random regular matrices with some prescribed zeros

I am given a set $N\subset\{1,\dotsc,n\}^2$. I need to generate random invertible $n\times n$-matrices $A=(a_{ij})$ such that $a_{ij}=0$ if $(i,j)\in N$. The set $N$ is chosen such that this is always ...
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1answer
53 views

What does “less random” mean?

Reading about random shuffle algorithms, I sometimes see the "randomness" of the method being discussed, and described as "less random" than a different algorithm. For example, if I take a random ...
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3answers
30 views

Calculate the winning probability when using two dice with a different number of sides

I have two players with one die. The first player throws a die between 1 and 125. The second player throws a die between 1 and 350. The winner is the person who gets the higher roll. How do I ...
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0answers
16 views

What is the sample space of a function of a random variable?

I know that a function of a random variable is itself a random variable. So, if $Y$ is a random variable, then $X = f(Y)$ is also a random variable. Assuming the sample space of $Y$ is ${y_1, y_2, ....
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1answer
53 views

Drawing random realisation from quantity with poisson error

How would I draw a random realisation of a variable with an upper and lower error determined from Poisson statistics using the Gehrels 1986 formula? See: http://adsabs.harvard.edu/abs/1986ApJ...303.....
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What exactly is a stationary distribution of a Markov Chain

I understand the mathematical definition of $ \pi P=\pi $, but exactly does this distribution signify? Let's say I have a 3x3 block, and I can only progress to the left, right, top and bottom, with ...
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1answer
24 views

Minimum number of random vectors needed to span a space

I am working with $\mathbb{R}^{nm}$ for some $n,m\geq3$. What is the minimum number of random vectors I need for them to span $\mathbb{R}^{nm}$ (in terms of $n$ and $m$)? I'm happy for this to ...
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2answers
24 views

How to use dice to randomly select from 10 choices? [duplicate]

Today I wanted to randomly select a number (0 to 9) using a six-faced dice. Because a single dice roll would not be sufficient (7, 8, 9, 0 would be missed), I determined that more than one dice roll ...
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0answers
26 views

Weighted Random Generator

I've done a number of searches for this and haven't found what I'm looking for, although it's quite possible I'm not using the correct terms. I'm trying to write some code (Javascript, but the math ...
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2answers
37 views

Generate random graphs with specific mean degree and mean edge weight

I need to generate random undirected graphs with the following characteristics: 24 nodes mean degree ranging between 1 and 23 mean edge weight ranging between 1 and 5 (weights must be integers) I ...
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2answers
129 views

Is the sequence of non repeating random numbers still random? [closed]

The original question was from a programming interview, they asked for a random player not playing same song until all other remaining songs have played in "Random" order. This question is asking for ...
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0answers
16 views

Understanding equality regrading expectation of random matrices

I'm reading the following article on Latent Tree Structures (I added a link at the end of the post) : "Spectral Methods for Learning Multivariate Latent Tree Structure". I'm trying to understand the ...
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1answer
29 views

Probability of three digits being the same

I have four people (n) and every time each is getting a random three digit combination (000-999). This means there are 1000 possible combinations (k). I want to know how probable it is for two or ...
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1answer
34 views

distribution according to random measures

Is a random probability measure a probability measure, i.e. if $X_i$ is random variable on some probability space $(\Omega,\mathcal F,\mathbb P)$ could its induced distribution be a random probability ...
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1answer
50 views

Proving $\mathbb{D}(\xi|\mathcal{D})=\mathbb{E}(\xi^2|\mathcal{D}) -(\mathbb{E}(\xi|\mathcal{D}))^2 $ [closed]

The conditional dispersion of random variable $\xi$ according $\sigma$-algebra $\mathcal{D}$ is a random variable: $\mathbb{D}(\xi|\mathcal{D})=\mathbb{E}((\xi - \mathbb{E}(\xi|\mathcal{D}))^2|\...
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event sequence generation based on probability distribution

Assume that there are five independent events, and the probability of each event is known, shown as follows, $P(x_i) = p_i, i=0,1,2,3,4$ There is one event in each time slot, while $T$ is the ...
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1answer
80 views

How to code oscillator driven by Gaussian white noise? Edit: How to convert ODE to a system of SDE's?

I have written some python code which was designed to try to solve the following differential equation: $$\ddot{x}+\omega_0^2x=\eta(t),$$ where $\eta(t)$ is the gaussian white noise, with mean 0 and ...
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1answer
43 views

time between transitions in continous time discrete state Markov process

Problem Statement: I want to compute the time between transitions in a birth-death model. As a simple example, consider that individuals are born with rate $\lambda$ and they die at rate $\sigma n$. ...
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1answer
72 views

How to make a circle within another circle?

I'm coding a "storm" for a battle royale map, and I'm trying to make a new safe zone (a perfect circle) inside of a preexisting circle. Right now, it looks like this: Link to circle picture This, ...
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2answers
35 views

Probability problem; adding elements to a list then picking from that list

It seems like a very simple problem but I couldn't figure out the solution myself (not homework) Simplified it's the following: ...
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0answers
11 views

Time between transitions in a birth death process with inhomogeneous rates

Question: Consider a continuous time Markov birth-death process describing a population $n = 0,1,2,\dots$, where the birth rate in state $n$ is $\lambda$ and the death rate in state $n$ is $\sigma n$....
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2answers
268 views

Will the energy of a randomly driven harmonic oscillator grow to infinity or oscillate about a finite value?

The equation of motion for an undamped harmonic oscillator, with driver $f=f(t)$ is given by: $$\ddot{x}+x=f.$$ Let the initial conditions be given by: $$x(0)=\dot{x}(0)=0.$$ If $f=\cos(t)$ ...
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0answers
45 views

Random Selection Paradox

I was asked a question in an aptitude test, the statement of which is as follows: "Out of 100 available equally likely choices we have to make 4 random selections. Goal is to have maximum randomness ...
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3answers
40 views

Finding a random position in the unit circle

Consider the unit circle (with radius $1$, because I can rescale it). Now, choose a random point inside it. How do you do this? The method I'm using is by choosing a random direction, from $0$ to $360$...
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2answers
51 views

Prove / Disprove that $E\big((X−a)^4\big)$ is minimized when $a=E(X)$.

Let $X$ be a random variable with moment up to order $4$. Prove / disprove that $E\big((X−a)^4\big)$ is minimized when $a=E(X)$. I've already proved that $E((X−a)^2)$ is minimized as such, but I'm ...
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1answer
65 views

Is it possible to randomly select a single member of $\mathbb N$? [duplicate]

The title is my question and the reason for asking it is the following. Define a set $\mathbb N (≤ n) \equiv$ {1,2,3, … , n} and define a “random selection” to be a selection in which each member ...
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1answer
30 views

Generalized Polya's Urn

In Polya's urn, we have $b$ black balls and $w$ white balls at time $t$. At time $t+1$, we have $b+1$ black balls with probability $\frac{b}{w+b}$ and $w+1$ white balls with probability $\frac{w}{w+b}$...
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0answers
37 views

Repeating random choice

Let's say I have 10 shirts (A to J) and I'd like to randomly wear a different one each day. So, the one I wore yesterday (let's say shirt J) has 0% chance of being chosen today; The one I wore the ...
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0answers
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Calculating expectations of concentrated random variables of bounded-differences type

Is there a nice general way of calculating the expectation variable for which I can derive concentration bounds using the method of bounded differences? I have seen quite a few application of the ...
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1answer
26 views

Generating Two Independent Standard Normal Variables

Image of problem I have a problem with this explanation, the book says we can generate Y1 Y2 from X1 X2 but when we want to answer questions about the distribution of X1 X2 we take arctan which ...
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1answer
43 views

st.petersburg paradox in python

I have been trying to do the St.Petersburg paradox( the player wins 2 dollars if tail appears on the first toss, 4 dollars if heads appear on the first toss and tails on the second, 8 dollars if heads ...
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0answers
24 views

Using randomly selected points uniformly distributed on the interval (0,1) find the volume of the unit sphere

I've been given this extra credit assignment to do in Matlab, but I don't understand the question. The part that I'm not clear about is where I have to satisfy the equation x+7+z>1. Can someone ...
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0answers
10 views

Thinning operation on a spatial binomial point process (BPP)

It is known that the thinning operation performed on a Poisson point process (PPP) results in a non-homogeneous PPP. Now, if we have a spatial BPP with N points distributed uniformly over some region ...
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2answers
61 views

Generating a random sparse hermitian matrix in Python

I'd like to find a way to generate random sparse hermitian matrices in Python, but don't really know how to do so efficiently. How would I go about doing this? Obviously, there are slow, ugly ways to ...
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1answer
186 views

Expected value in multiple rounds

I am doing an exercise that sounds like: The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land ...
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0answers
11 views

Help calculating second order distribution for a continuous stochastic process

I'm really stuck on this problem, and appreciate any help. Problem: Let $\gamma$ be a random number, chosen with uniform probability in the interval $[0,2\pi]$. We define the stochastic process $X(t)...
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3answers
83 views

Create unique one to one number from 2 numbers

A smilar question has been asked before Create unique number from 2 numbers. is there some way to create unique number from 2 positive integer numbers? Result must be unique even for these pairs: 2 ...
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0answers
52 views

Generate random numbers with conditions using maxima (cas)

I want to generate (multiple) random numbers from a given number class with extra conditions. (for automatic generation of exercises) e.g.: generate "a" out of natural Numbers which are dividible by ...
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0answers
31 views

Working out expectation of a random sample.

I have the problem: Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has mean $μ$ and variance $σ^2$. Find $\mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T ...
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2answers
43 views

Two aspects of randomness

Consider a random sequence of integers 1, 4, 3, 8, 2, 5, 3, 8 ... The only sufficient condition for the sequence to be random is its unpredictability ie. probability of any number coming next ...
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2answers
30 views

Probability of picking 3 playing cards that belong to different suits

If you have 52 playing cards with 4 different suits (13 spades, 13 clubs, 13 hearts, and 13 diamonds), what is the probability of picking 3 random cards that are all from a different suit? I tried ...
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0answers
21 views

What is the mean of a random number with one exclusive bound?

If I have a random number between 0 and 1 inclusive, the mean is 0.5. If both are exclusive, the distance from 0.5 to 0 and 0.5 to 1 are the same, so 0.5 is still the mean. But if 0 is inclusive and 1 ...
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0answers
48 views

Expected value and variance of random variable on some terms(dates?)

I have a exercise that sounds like this: Find the expected value and the variance of the random variable X with natural values in terms of: a)generating function P b)generating function Q Excercise ...