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

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0answers
32 views

Help!!!!!!!!!!!!!! [on hold]

1. Assume that books from a certain publisher have an average of one misprint every 20 pages. (a) What is the probability that a given page has two or more misprints? (b) What is the probability that ...
0
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2answers
22 views

probability: arithmetic with random variables.

I have a question of using arithmetic on random variables. Please refer to the following question, to which I will present my solution using the arithmetic (which I thought it's correct but actually ...
1
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1answer
18 views

Random points in sphere with probability p(r)

How to pick random uniformly distributed points in a sphere has been asked before. The difference is that I don't want uniform distribution, rather I would like the number density to scale by ...
1
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1answer
30 views

{Probability}: choosing keys from a pool without replacement

The OP is trying to understand the following question. The OP understand that if you can always write out the term $$P(X=k) \implies (1-\frac{1}{N})(1-\frac{1}{N-1})\cdots(1-\frac{1}{N-k+1}),$$ ...
0
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0answers
16 views

Matlab function that returns samples of random process

Given an autocorrelation function for a random process $X(t)$, how could I write a Matlab function that returns samples of $X(t)$? (specifically $X(n\cdot \Delta t)$, $n=0,1...,N$ where ...
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0answers
6 views

Random numbers with groupings

I have 9 items, I need to pick a random item and I would like each item to be just as likely as the others to be chosen. I'm assuming my RNG is perfectly. Currently I am picking a random number ...
0
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1answer
50 views

Probability: deviation from the mean

I am having trouble to understand the following. If $S_n=X_1+X_2+......+X_n$, where X_1,X_2 are Bernouli (p). I don't understand this. So you get an intermediate point Constant* sqrt(n). To the ...
2
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0answers
32 views

Can the chaotic motion of a double,triple,… pendulum be used as a source of randomness?

I've been playing with this animation, and I was curious whether the chaotic motion could be used as a source of randomness. It seems that if the motion is unpredictable (i.e. nondeterministic), then ...
2
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2answers
67 views

Is a number chosen at random necessarily irrational?

If I were to pick a number completely at random in the range [0,1), it seems to me that number would be irrational. After all, there are a countably infinite number of rationals between zero and one, ...
0
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1answer
21 views

Power spectral density of a stationary random process

The stationary random process X(t) has a power spectral density denoted by Sx(f). a. What is the psd of Y(t) = X(t) - X(t-T)? b. What is the psd of Z(t) = X'(t) - X(t)? What should the approach ...
0
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1answer
28 views

Random sample and probability

A random sample of 325 new toothbrushes showed that 14 were defective. What is the estimate of the probability that a new toothbrush is not defective? Either a toothbrush is defective or not. What is ...
110
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23answers
9k views

Is an SD card a fair coin… to me?

This morning, I wanted to flip a coin to make a decision but no coins were in reach. There was however an SD card on my desk: Given that I don't know the bias of this SD card, would flipping it be ...
1
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0answers
22 views

Generate correlated random numbers precisely

Let's assume I want to generate k samples of n random numbers, that are correlated according to a given correlation matrix C (e.g. $n = 3$): ...
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0answers
15 views

Probability in a weighted Random

This is actually a question that came up whilst programming, but i figured this is more a question for the mathematicans: in a database have a set of roughly 500 entries. now i want to get 10 random ...
2
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0answers
19 views

testing hardware random number generators? [closed]

1)I would like to know how to test hardware random number generators. 2)What techniques ,tools or tricks to solve the problem ? 3)Any practical difficulties, implementation complexities etc
1
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1answer
28 views

Can 3 random variables have pairwise correlation -1?

Can 3 random variables X, Y, Z have pairwise correlation -1? This seems to be easy question, but I just got confused over this.
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0answers
16 views

Diameter of graph formed by pairwise intersections of random chords in a circle

Given n random chords in the circle (a random chord is chosen by specifying both endpoints uniformly randomly from the circumference), form a graph G on n nodes such that an edge exists between i and ...
0
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1answer
55 views

Sample uniform direction within cone

My question is pretty much the same as this question below, however I came up with a potential solution to this problem that I didn't see an answer to in the other question and I was wondering if it ...
0
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1answer
33 views

Given the distribution of a random variable $R$, who do you get a uniform random variable $U$?

Let us say you have a random variable $R$. How would one generate a uniform random variable $U$, with the maximum possible entropy (or infinite entropy, if $R$ has such)? (For simplicity, you may ...
0
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1answer
61 views

sum of independent Rayleigh random variables [closed]

How do I find the probability density distribution (pdf) of the sum of independent Rayleigh random variables (whose probability density functions are known)? where is the reference? Could anybody ...
0
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1answer
19 views

Density on the square, expected value

Let $f: [0,1]^2 \rightarrow \Bbb R^{+}$ a density function on the square. I suppose that the random variable $X=(X_1,X_2)$ has the density f with respect to the lebesgue measure. I denote ...
0
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1answer
29 views

Moments of Geometric Random Variable

Let $X$ be a geometric random variable i.e. it represents the number of consecutive failures before you get the first success where the success probability is $\rho$. We know $E[X] = 1/\rho$ and ...
0
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0answers
20 views

Understanding graph obtained from Monte-Carlo simulations

I am running a Monte Carlo Simulation where I sample from about 65 Normal Distributions. I also keep track of the probability associated with each sample by approximating a thin area in the Normal ...
0
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1answer
32 views

Measuring degrees of randomness

Imagine, for simplicity's sake, that we have a set of numbers, each equal to either 0 or 1. Let's call each a bit. Rationally, if the set is completely random, and reasonably large, the probability ...
4
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0answers
122 views

Asymptotics of sum of binomial distributions

Definition 1: For any random variable $X$, we define $Bin(p,X)$ as a variable with binomial distribution having parameters $p$ and $X$. Definition 2: For all $i \in \mathbb{N}$, define recursively ...
1
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2answers
34 views

How to create a random number generator that is completely random.

I'm trying to write an autonomous music composition program that makes use of many random number generators in order to make seemingly random melodies but I have no clue how to formulate a rigorous ...
1
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1answer
28 views

How to Create a Plane Inside A Cube

I have a $e \times e \times e$ cube and I want to create random planes with equation $ax + by + cz + d = 0$ inside this cube. I will put random points on those randomly created planes as well. Here ...
0
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2answers
41 views

Consider throwing two six-sided dice.

Let X be the sum of the two values and let Y be the product of the two values. What is the value of P(Y = i) for i = 1,2,3...36. I am having trouble approaching this problem. We are learning about ...
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1answer
84 views

Solution of equation of binomial random variables

Is it possible to find the probability distribution of the random variable $X$ that solves the following equation? $$ X = Bin(X, p) + Bin(X, 1-p), $$ where $Bin(X,p)$ is a random variable distributed ...
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0answers
24 views

Random sample taken, what is probability?

It was determined that 22% of all stock investors are retired people. In addition, 38% of all U.S. adults invest in mutual funds. Suppose a random sample of 20 stock investors is taken. a. What is ...
13
votes
2answers
203 views

$e$ popping up in topic I'm unfamiliar with

I programmed up a little algorithm that goes like this: Fix two positive, real numbers, call them $\alpha$ and $\beta$. Generate a new, random, real number, $x \in [0,1]$ Set $\alpha$ = ...
0
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1answer
23 views

Probability of occurrence after Latin Hypercube sampling and then random sampling

I am using Latin Hypercube sampling to obtain numbers from a Normally Distributed set of data, so that I get a uniform spread of numbers across the Normal Distribution. I then select a number at ...
0
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1answer
14 views

Probability of numbers within a Latin Hypercube

What is the probability of occurrence of numbers in a Latin Hypercube? If I have a 1 dimensional Latin Hypercube of 1000 numbers would the probability of each number just be 1/1000? Essentially, I am ...
0
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1answer
31 views

Generating Different types of Matrices in Matlab

I am working on a project for a numerical methods class comparing two iterative methods for solving $Ax=b$, and I was wondering what type of functions Matlab has for generating arbitrarily large ...
2
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0answers
53 views

Random walk with $\sum_{n=1}^{\infty} \frac{1}{n} \mathbb{P}\{ S_n > 0 \} < \infty$

Consider a random walk started at $S_0=0$, denoted $S_n = \sum_{k=1}^{n}X_k$, where $X_1$, $X_2$... are the i.i.d increments. If we have $\sum_{n=1}^{\infty} \frac{1}{n} \mathbb{P}\{ S_n > 0 \} ...
1
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1answer
37 views

Probability of random variable in Normal Distribution

I've been talking to my lecturer about choosing random values from a Normal Distribution and he says the following: "Roughly 68% of expected values $ \in (\mu-\sigma,\mu + \sigma)$ does not imply ...
1
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1answer
22 views

Randomized algorithm to determine if a polynomial over $\mathbb{Z}/p$ is irreducible

Is there an efficient (possibly randomized) algorithm to determine if a given polynomial $p(x) \in \mathbb{Z}/p\mathbb{Z}[n]$ is irreducible?
1
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0answers
35 views

determining the next random number pseudorandom number generator?

I have given 3 numbers let's say basic example x_0=5, x_1=6 and x_2=2 and modulus p is 7, ...
1
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0answers
35 views

Random operators [duplicate]

Let $(\Omega, \mathcal F,P)$ be a probability spaces and $H$ be a Hilbert space. By a random operator $A$ from $H$ to $H$ we mean a linear continuous mapping from $H$ into the Frechet space $L_0^H ...
1
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1answer
29 views

Algorithms for non-random but equidistributed ways to fill up a Cartesian plane

In pages 90-91 of this book the authors talk about uniform, but not necessarily normally distributed random ways to fill up a Cartesian grid. For example, in the attached images. These are the ...
0
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1answer
31 views

Random walk in nXn grid. probability reaching top row

A woman walks randomly on a nxn grid starting at the point (1,1) (the lower left corner). Each minute the women moves either to the right or up (so (a,b)-> (a+1,b) or (a,b)->(a,b+1). Her walk ends ...
2
votes
1answer
36 views

Probability question (grid)

Say I have a grid of 10x7. Every square of that grid is empty. Then, 20 squares, chosen at random, are filled (a square can only be filled once, so no duplicates allowed). What is the probability of ...
2
votes
3answers
75 views

Probability of collecting all 5 different items at random with different weights

There are 5 different items in a set, each with a weighted chance of being rolled randomly [A-E]. The weights add up to 100%. $$A=5\%, B=10\%, C=15\%, D=30\%, E=40\%$$ You get 1 item every roll no ...
2
votes
0answers
40 views

Random pair generation?

Suppose there are 6000 people, there will be a combination of $$\binom{6000}{2}$$ ways for 2 people to be chosen out. Now the task is to randomly choose 5000 pairs of people in the total 6000 ...
0
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1answer
25 views

Generating Random Serialnumber with least similarity

I want to generate 16-digits hexadecimal serial-number like: F204-8BE2-17A2-CFF3. (This pattern give me 16^16 distinct serial-number But I don't need all of them as I describe below) I need an idea ...
0
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1answer
27 views

What is a pdf of Gaussian noise convoluted with a sine wave?

I realize that it is relatively easy to compute the variance of an AWGN convoluted with a sine-wave through auto-correlation function. My question is how do I find the pdf if I know the variance and ...
-1
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1answer
36 views

random number usage in filling 2d array

Below is a small program which has 2-3 Math concepts involved we have 2d array of $i$ width and $j$ height, idea of this program is to fill ...
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2answers
19 views

Show that $Cov(X,Y) \geq -23$

if $X,Y$ are two random variables and: $Var(X) = Var( Y) = 23$ how can i show that $Cov(X,Y)\geq -23$ can someone give me some hints on how to show it?(not an answer) i know that $Cov(X,Y) = E(XY) ...
0
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2answers
46 views

the maximum of two random variable

The maximum of two random varibles $X$ and $Y$ is: $$Z=\max\{X,Y\}= \begin{cases} X & \text{if } X \geq Y \\ Y & \text{if } Y \geq X \end{cases}$$ I don't understand. So if I roll two dice, ...
3
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0answers
34 views

Can I solve this probabilistic problem or do I need more data?

This problem happened to me almost 3 years ago and I just discovered this site by luck, so I want some help to know if this problem is solvable (if so, I would like to know how to solve it as well as ...