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

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1answer
15 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
votes
1answer
21 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 ...
30
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3answers
5k 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 ...
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1answer
26 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
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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
979 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 ...
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0answers
14 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
14 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
votes
1answer
70 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
30 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
36 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 :)
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2answers
27 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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0answers
49 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 ...
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0answers
13 views

Generating nonsense, but pronounceable words [closed]

Using nonsense, but pronounceable words can be useful sometimes, for example to test search engines, etc. Is using generative grammars, and a random word generator algorithm a good idea for picking a ...
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2answers
31 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
23 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
39 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?
1
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1answer
34 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
votes
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
21 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
35 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
23 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
19 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 ...
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0answers
34 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
12 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
votes
2answers
79 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
39 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
34 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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votes
0answers
14 views

Combing properties of Random Hashes and passing the dieharder test

I have two streams of numbers, range A are 64 bit numbers and may be largely sequential. In fact one of the issues is I don't know the full range and properties of these numbers. The other range (B) ...
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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
25 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
52 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
38 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
30 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 $~$ ...
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0answers
20 views

Ideal shrinking of discrete randomness source

I have a discrete randomness source that emits random integer numbers in range [0..N) with uniform distribution. I need to reduce this distribution, limiting it to ...
3
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1answer
71 views

What constitutes randomness?

To begin with, I am not a mathematician, so the question might sound dumb :) Anyway, I have been playing 2048 and thinking on randomness and some things just do not seem very straight to me, when ...
2
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0answers
30 views

Knuth shuffle : Is there a reciprocal to the factorial?

I have looked into the Knuth collection shuffle algorithm with pseudorandom number generators. They say that a PRNG with a seed state of $19937$ bits (like one of the Mersenne Twisters) can shuffle a ...
2
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1answer
67 views

Primitive polynomials in LFSRs

I need help proving the following theorem. I found it many books but on every single one it says that they omit the proof because it is in every good textbook. THM Let $c(x)$ be a connection ...
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2answers
53 views

How to tell if a set is cyclic

I've been reading a bit about pseudo-random number generators lately. My understanding is that they generate numbers that seem random for all practical purposes but they are actually just really big ...
0
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1answer
40 views

probabilities for obtaining 3 dice result

I am developing an app that needs a 3 dice result and there are two methods I can use: method a) create a matrix of 216 possible combinations and choose 1 randomly method b) or generate 3 ...
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0answers
11 views

Sampling a path in graph where each edge has a fitness

I'm writing an heuristic algorithm for the Travelling Salesman Problem. In one step, I have to generate a random path of length $n$ in a graph $G$. There is a real number in $[0, 1]$ associated to ...
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3answers
60 views

Convolution of maximum and minimum of uniform random variables

Let $X_1,\ldots, X_n$ be $n$ independent random variables uniformly distributed on $[0,1]$. Let be $Y=\min(X_i)$ and $Z=\max(X_i) $. Calculate the cdf of $(Y,Z)$ and verify $(Y,Z)$ has independent ...
1
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1answer
49 views

How to place random points on an egg?

While I was having breakfast this morning, I thought: "I know how to put random points on a sphere or a torus, but how to place random points on an egg (with uniform probability with respect to any ...
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1answer
38 views

Probability Density of Convolution of Two Random Processes or Variables

Suppose that we have two stationary random processes $x(t)$ and $y(t)$ with probability density functions $f_{x}(x)$ and $f_{y}(y)$ respectively. Now suppose we form: $z(t) = x(t) \ast y(t)$ What is ...
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3answers
48 views

Using loop to approximate pi (Monte Carlo, MATLAB)

I've written the following code, based on a for loop to approximate the number pi using the Monte-Carlo-method for 100, 1000, 10000 and 100000 random points. ...
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2answers
60 views

Alice and Bob card game

I came across this puzzle online in an online Princeton thingy (course?): Alice writes down two integers between 0 and 100 on two cards. Bob gets to select one of the two cards and see its value. ...
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0answers
20 views

Mathematically safe, open TAN generation and verification

For an upcoming Arduino project I need to generate, distribute and verify TANs (transaction authentication numbers). Let me explain (and assume for a second this is happening on a bigger computer). I ...
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0answers
33 views

Calculate expected value E(|x-y|^2)

I have two random variables (X and Y) that are uniformly distributed from 2.16 to 6.81 both. And I need to find E(|x-y|^2). Is this correct: ...
3
votes
4answers
139 views

Does this sum converge or diverge?

Does the infinite sum $\large{\sum_{n=1}^\infty \frac{1}{n^{x_{\small{n}}}}}$ converge if $x_n$ is a random variable (generated within each term) that takes values between $0$ and $2$ with equal ...