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

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15 views

Random variable variance

I have the model yi=β1+β2Xi+ui where ui∼iid N(0,σ2). I estimate β1 and β2 by drawing a straight line between the first (x1,y1) and last dot (xn,yn). So, β̂ 2 will be the slope of this straight line. ...
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0answers
22 views

The probability that uniformly distributed integers sum to a given integer

A recent CTF had a problem involving the summation of randomly distributed integers. Specifically: Consider a set $\{X_m\}$ of $M$ integers uniformly selected (with replacement) from the set of ...
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0answers
8 views

What does one-cut random matrix mean?

I am quite new to random matrix theory and recently I encountered the so-called "one-cut random matrix model" and even "two-cut" in physics. So what exactly does it mean?
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1answer
21 views

Translate the word phrase into a variable expression. [on hold]

The number $a$ is increased by the number $b$. A. $a-b$ D. $a \div b$ C. $a+b$ D. $a \times b$
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2answers
19 views

Random number distribution from a different distribution

Suppose I have a random number generator that generates random numbers $x$ with a normal distribution $p(x) \propto e^{-x^2}$ (modulo normalization, but lets keep it simple). Now, out of these ...
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9 views

Is it possible to use multiple time scale algorithm here?

Suppose a random sequence is being generated (the next term generated depends on the previous term, but we don't know any distribution) until we hit some specific number. We want to calculate the ...
-1
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0answers
28 views

A simple formula for pseudo-random binary string

I'm trying to illustrate the concept of Kolmogorov complexity by comparing two seemingly-random binary strings: while one is truly random, the other can be created by a program smaller than its ...
0
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1answer
15 views

Generate random results in a continuous field

How can we generate random results for a field like economical predictions where there is no limited number of results (contrary to a coin with 2 results) and also contrary to a random walk with steps ...
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1answer
18 views

How Many Unique Character String Can Be Made From 62 Characters?

I'm working on a programming algorithm and need a little math help. I'm in 10th grade and I think the question I'm asking is actually a permutation and combination logic question. Okay, so I've 62 ...
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5answers
609 views

Is the product of uniformly distributed numbers, uniformly distributed too?

My question is simple, I think. If we took two random natural numbers $a$ and $b$ uniformly distributed in a specific range $[c,d]$, is $ab$ a uniformly distributed too? What if $a$ and $b$ are not ...
2
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2answers
44 views

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 ...
0
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0answers
10 views

What it means by “asymptotic normality” properties of a random matrix?

I know that for the case of a random variable and a random vector, one can using (multivariate) density of normal distribution and concepts of convergence to define an asymptotic normality of a random ...
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0answers
26 views

Understanding Sobol sequences

Can someone explain to me in simple terms, how Sobol sequences work? The wikipedia article is fairly technical. They look pretty interesting. So I shall describe (whatever little I know) in short the ...
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0answers
6 views

Distribution of cut-off pseudo random numbers via linear congruential generator

I am currently using congruential prng as described here: Wikipedia. Now I need pseudo random numbers in the interval $[0, N), n < m$ where $m$ is the divisor of the modulus calculation. I want to ...
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0answers
35 views

Is the probability of variable independence = 0?

I understand the concept of independence to be dichotomous- events are either independent or dependent. And while there are infinitely many ways for events to be dependent and only one way to be ...
1
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2answers
41 views

What is the expected value of this sum (drawing slips from a bag)?

Suppose there are thirteen slips in a bag, labelled 1-13. If I draw a 10, 11, 12, or 13 then I stop adding to the sum and return the sum. If not, I add the number I draw to the current sum and place ...
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0answers
35 views

Dimensional Consistency in Grids used in Optimization

I am working on an optimization problem in the research I am doing and my partner and I have found that in order to quickly converge on a solution using a specific PSO (the firefly algorithm - it's ...
1
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1answer
20 views

Find the probability $P[ x(t) \le 1]$ where $x(t)$ is a filtered Poisson process (rect pulses)

I can't understand the following question: "The random process x(t) is defined as $$x(t) = \sum_{n=- \infty}^{+\infty} rect(\frac{t-\tau_{n}}{T}) \quad ,\quad t \ \epsilon \ (R)$$ where {$\tau_{n}$} ...
2
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1answer
24 views

The probability of getting a certain image by random pixelation

Well, seeing that I'm terribly bad at math I don't know how to solve this, I'll try to explain, excuse me if I sound dumb. Just suppose that I've got a photo/image with 320x240 resolution and 24 bit ...
31
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3answers
6k views

Making 400k random choices from 400k samples seems to always end up with 63% distinct choices, why?

I have a very simple simulation program, the sequence is: Create an array of 400k elements Use a PRNG to pick an index, and mark the element (repeat 400k times) Count number of marked elements. An ...
1
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1answer
30 views

Random points inside a convex polytope

Given a convex polytope, defined by set of vertices $P = \{\mathbf{x}^{(i)}\}_{i = 1}^n, x^{(i)} = (x^{(i)}_1, x^{(i)}_2, \dots, x^{(i)}_d): \operatorname{conv}(P) = P$. How to generate uniformely ...
2
votes
0answers
58 views

Randomness in a sequence

For a function $f$ consider a random sequence $a_{n+1}$ can be either $a_n+f(a_n)$ or $a_n-f(a_n)$ Given that the next term in the sequence is subtracting $f(a_n)$ from the previous term 50% of the ...
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2answers
1k views

What is golden ratio doing in this computer code?

In this file (related to random number generation), there is following line: private const int MSEED = 161803398; which reminds on golden ratio. How come ...
12
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2answers
997 views

Apparent Paradox in the Idea of Random Numbers

This question is a bit less than rigorous, but it's only because I don't know how to formulate it rigorously. Suppose there was some machine, or function, or whatever that could output a random ...
0
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0answers
15 views

Spherical Sampling of Projected Disk

Given a 2D solid disk centered at some 3D point $\vec{x}$ with radius $r$ and normal $\vec{N}$, I need to compute a random unit vector from the origin that hits the disk. The vector needs to be ...
0
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1answer
15 views

PRNG to generate a known set of values

Say I want the first N numbers generated by PRNG to be some list [n1, n2, n3, n1, nx...]. Is there any way to accomplish this (basically find the appropriate seed ...
3
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1answer
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 ...
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1answer
32 views

All combinations for a picking from a set of three colored balls

I can't find this exact question. The specific question I have is this: If you have a bag with one red, one blue, and one green ball, the chance of picking any particular one is 1/3. Simple enough. ...
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2answers
37 views

Exercise on Random Variables

I´m struggling with a random variable exercise of a book I´m reading. Anyone has an idea of how to approach this problem? Thanks in advance :)
2
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2answers
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 ...
0
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0answers
54 views

Probability Question involving Probability Mass Function/Random Variables

Problem: When a paging system transmits a message, the probability that it will be received correctly by the appropriate pager is p. To ensure that the message is correctly received at least once, the ...
0
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2answers
34 views

Calculate random integer inside a range of real numbers

$$F : \Bbb R \times \Bbb R \rightarrow \Bbb N $$ $$F(\text{minReal},\ \text{maxReal}) = \text{randomInt} \in \left[\text{minReal},\ \text{maxReal}\right] $$ Let $r \in [0, 1)$ be a random value. How ...
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0answers
24 views

Select machines to minimise latencies between them

I am working in an optimisation problem. I am still trying to model it and solve it. The problem is: There is a number of different types of virtual machines. Each type has different hourly cost ...
0
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2answers
41 views

Expected value: Product of integers in a range

What is the expected value of $f(x)^k = f(x) f(x) \cdots f(x)$ if $f(x)$ is a function, that returns a random integer between $0$ and $x - 1$ inclusive?
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1answer
37 views

Generate random numbers with a modified PERT distribution

I want to generate random numbers based on the modified PERT distribution. The modified PERT distribution is a special case of the beta distribution and is defined as: $$f_X(x) = ...
3
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0answers
31 views

What is the most important test for a uniform random number generator?

What is the most important test for a uniform random number generator ? Is there a single most important test or a set? I am a using some analytically arrived at answers to probability problems and ...
1
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1answer
22 views

Creating a bivariate distribution from two independent variables

If you have two random variables that are independent say $X\sim f_X (vars)$ and $Y \sim f_Y (vars)$. Is this a way to produce a bivariate distribution $f_{(X,Y)}$? $f_{(X,Y)} = p(X=x \cap Y=y) = ...
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2answers
37 views

Probability Random Variable question Need Help Please

You have a set of ten light bulbs - the lifetime of each of them being given by an exponential RV with mean 1000 hrs. Find the probability that.... (a) at least 7 of the bulbs function for 1500 or ...
2
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1answer
26 views

Why is the formula for generating Van der Corput sequences called an Inverse Radical Function?

The Van de Corput sequence can be generated using the following formula: $\phi_b(n) = \sum_{i=1}^N { a_j \over b^{i-1}}.$ where this can be defined as the "one-dimensional sequence defined by the ...
0
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0answers
21 views

mean square convergence vs almost sure convergence

I saw a few examples that show that almost sure convergence doesn't imply convergence in mean square. Can anyone find an example of a random series that converges in mean square but doesn't converge ...
0
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0answers
36 views

Proving properties of Random Graphs

I am asking the question on a slightly abstract level and it may depend on the specifics but it would be great to have related references or ideas. Consider the random graph model $G_{n,p}$ where its ...
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0answers
13 views

How to normalise logarithm depending on the size of the range of possible values

I'm attempting to write a function which can be used to generate weighted random numbers between a set range, the size of which can arbitrarily grow and shrink, depending on some modifying value to ...
3
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2answers
87 views

What is the probability of a specific sequence of 11 digits occurring in a random sequence of one billion digits?

This isn't homework, I'm actually (please don't ask me why) wondering how likely it is that any particular 11-digit telephone number will occur in the first billion digits of pi. My probability course ...
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0answers
40 views

Why does a Gaussian process have a gradient whose determinant is Gaussian?

I'm trying to understand something in Adler and Taylor's book, Random Fields and Geometry. Let $T \subset \mathbb{R}^N$ be a compact parameter set (for simplicity, suppose it is a closed hypercube) ...
0
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0answers
37 views

Law of large numbers with random weights

Let $\mu_i$ be i.i.d. RVs with mean zero, and let $a_i$ be random weights that are not independent and are not identically distributed, $i=1,...,N$. $\mu_i$ is orthogonal to $a_j\;\forall j$. Is ...
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8answers
2k views

3 random numbers to describe point on a sphere [duplicate]

I'm currently working on a problem involving computer graphics and got into a discussion about whatever or not constructing a 3d vector out of 3 random points uniformly distributed points between -1 ...
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0answers
26 views

Random sampling and i.i.d.

Can you help me to clarify the following concepts by stating whether what I have written below is right or wrong? -random sampling: units are drawn from the population with a known probability of ...
2
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0answers
54 views

“Alice and Bob” problem with matrices

Alice has a binary matrix $A$, and Bob has a binary matrix $B$. Both matrices are of size $n \times n$. Alice and Bob want to check if the matrices are equal except for exactly $1$ entry. Alice has to ...
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1answer
43 views

How does a pdf of the difference of two random variables relate to the pdf of each random variable

Let $T_1$ and $T_2$ be non-negative continuous random variables (rv) denoted in the form $T_i = \mu_i + \sigma_i X_i$ for $i=1,2$ where \begin{eqnarray*} T_{1} &=&\mu _{1}+\sigma _{1}X_{1} \\ ...
0
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1answer
39 views

Average norm of a N-dimensional vector given by a normal distribution

I'm interested in knowing what is the expected value of the norm of a vector obtained from a gaussian distribution in function of the number of dimensions $N$ and $\sigma$, i.e: $E[||x||_2]$, $x $~$ ...