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

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1answer
18 views

Which is the probability?

On the Swedish SAT test, you have 5 options for every question where precisely one option is correct. If you answer randomly, what is the probability that your score will be 0.9 if the maximum score ...
2
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1answer
32 views

Intuition on Martin-Löf-Test for finite strings

The followng example is from An Introduction to Kolmogorov Complexity and Its Applications, Example 2.4.1. and is concerned with Martin-Löf-Tests for finite strings: A string $x_1 x_2 \ldots x_n$ ...
0
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1answer
27 views

Partition-based entropy of a sequence

The entropy $H$ of a discrete random variable $X$ is defined by $$H(X)=E[I(X)]=\sum_xP(x)I(x)=\sum_xP(x)\log P(x)^{-1}$$ where $x$ are the possible values of $X$, $P(x)$ is the probability of $x$, ...
1
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3answers
42 views

Intuition behind generating continuous random valiables

If we have a random variable $X$ with cumulative distribution function $F$ that is strictly ascending and we manage to find the inverse we can generate an instance $x_1$ from a uniformly distributed ...
1
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1answer
36 views

Generate random number according to any equation

So I'm after a random number generator where the probabilities of a number occurring in some range is matched to some function. Only really looking at functions with nice integrals (for simplicity ...
0
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0answers
14 views

continuous random variable - pth percentile

Let X be a loss random variable with cdf $$ F(x) = \left\{ \begin{array}{ll} 1-(θ/θ+x)^α & \textrm{for $x≥0$}\\ 0 & \textrm{for $x<0$}\\ \end{array} \right. $$ The 10th percentile is θ−k. ...
3
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0answers
23 views

How to sample from a convex hull?

Let us consider a couple of points $x^{(i)}\in \mathbb{R}^m$ where $i=1,\dots,n$. Convex hull is defined as $$ C = \left\{\sum_{i=1}^{m} \alpha_i x^{(i)} \mathrel{\Bigg|} (\forall i: \alpha_i\ge ...
1
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1answer
30 views

Shuffling the columns of a matrix

Suppose I have an $N\times k$ matrix: $$\begin{bmatrix}a_{1,1} & \cdots & a_{N,1} \\ \vdots & \ddots & \vdots \\ a_{1,k} & \cdots & a_{N,k} \end{bmatrix}$$ Is there a ...
0
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0answers
13 views

Is two single byte random codes more secure than a single word random code?

I am trying to create secret keys for a post so users can edit them without entering password. Typically I use two secret IDs to reference a post, ID1=8 byte long random code ID2=8 byte ...
3
votes
2answers
65 views

A single, good test for a random number generator?

I'm chasing a bug in the RNG for a well-known programming language under certain pathological inputs. There is an obvious pattern in this pathological case, apparent with very small n (~ 10000), and ...
0
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1answer
30 views

Hitting all bins at least once

$m$ balls are thrown at a total of $n$ bins. Each ball will fall into exactly one randomly chosen bin with each throw. What is the probability that each bin is hit at least once (contains at least one ...
0
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1answer
22 views

Uniform random number generation

Given a uniform random number generator that generates integers between any given range, a n-tuple $b$, and an integer $c$, how can one uniformly generate n-tuples ($x$) that meet the following ...
6
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0answers
74 views

How to attack universal hash function based on finite-field arithmetic?

As per the Recursive n-gram hashing is pairwise independent, at best paper, I want to use the algorithm described in chapter 6 and 7 (page 7 - 10). The hash works as follows: Define a random ...
0
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0answers
16 views

Function/algorithm to generate a random walk on a graph

I'm looking for a graph function or an algorithm that can generate a random fluctuating random walk that will eventually converge between the value of y = 0 and y = 1, more or less after a number of ...
1
vote
1answer
46 views

Randomness in pi and other irrational numbers [duplicate]

This is a post I read about pi while looking for stuff about tau -which is two times as much as pi. This makes me wonder, why does only pi contain such randomness? Don't other non-repeating and ...
2
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0answers
27 views

A set of conditions to prove or disprove randomness

I am trying to understand the heuristic connection between fitting a normal distribution to a dataset and the definition of what constitutes a random process. If a normal distribution fits your ...
1
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4answers
56 views

The normal distribution is a common model of randomness

Can someone please comment/elaborate on the statement: "The normal distribution is a common model of randomness." I would like to understand it more deeply. Source: Perhaps someone can point me ...
0
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2answers
39 views

Worst case binary search

Suppose you play a game with a computer program where you guess a number between 0 and 1 and the computer uses binary search to search for your number. My question is what is the best number to ...
0
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0answers
10 views

How to define a one-parameter family of probability distributions

I am trying to evaluate a noise-source as a means of providing entropy to a random number generator. I am running into trouble when it comes to determining the probability distribution that has the ...
0
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2answers
59 views

Random equation-does it make sense?

What is the probability that the equation $$x^2+2bx+c=0$$ has real roots? Answer is exactly $1$. (or $100$%) For example: if $b=1$ and $c=2$ roots are complex. Does it make sense? If $P(A)=0$, then ...
0
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0answers
10 views

Can PRNGs and RNGs work as different RNG/PRNGs?

I think the title was pretty bad but I'll explain. Let a RNG-n and a PRNG-n be a random integer generator and pseudo-random integer generator respectively that both randomizes integers from 1 to n (1 ...
1
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2answers
64 views

How many bit-flips are required to achieve random distribution?

If I have a binary number W bits wide, initially all set to zero, and I repeatedly pick a random bit and toggle it from zero to one or vice versa, how many times would I need to do this to achieve ...
1
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1answer
13 views

Dynamic weighed probability

If I have a list of objects, and want [programmatically] to randomly pull one out, I can simply choose a random number representing a valid index within the range of elements of the list: ...
2
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2answers
43 views

Can this probability mechanic be used in a simulated gambling scenario?

This question is a bit complicated, so please bear with me. I realized this question after watching this video from the popular Youtube channel Numberphile. This video claims that when two random ...
0
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0answers
8 views

Linear congruential generator, $\pmod p$ a prime

I'm interested in pseudorandom generators of the kind $$ x_n = a\cdot x_{n-1} + c \pmod n $$ where $n$ is prime (for concurrency reasons). However, the ones I have found in the literature either have ...
2
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1answer
32 views

Unknown random number generator

I recently browsed through someone else's code and found a section where a pseudo random number generator is implemented. I know that random number generation is not an easy task, some even regard as ...
0
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1answer
22 views

Randomization and probability with constraints

The probability of getting a specific suit out of a deck is 13/52. Once we have one suit (color) selected the probability is 12/51 for that suit and 13/51 for others. This much is obvious. Now ...
1
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1answer
13 views

Random Numbers and Binomial Distribution

Let's say we have generated n=100000 numbers from a set: {1, 2, ..., 50}. Let X a discrete random variable that expresses the number that 1 appears. Then X~Binomial(n,p), where n=100.000 and p=1/50 ...
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0answers
14 views

Non-linearity on Random Sequence

I recently incorrectly assumed that applying a non-linear operation on a completely uncorrelated sequence would yield an uncorrelated sequence. Turns out that it is trivially easy to show that this ...
7
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3answers
124 views

Random Sequence of Alternating Increase/Decrease Numbers

The problem statement: Repeatedly pick a random number (uniformly-distributed) between $0$ and $1$. Keeping going while the second number is smaller than the first, the third number is larger than the ...
0
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2answers
32 views

Random 4D vector

I'd like to generate random 4D vectors. Their length must be 1. A random 2D vector can be created like so: ...
2
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4answers
84 views

What is the statistical equilibrium for this simulation of happy bubbles?

Happy Bubbles I hope this is not too specific or practical, but I just made a simulation of sorts and seem to have hit quite close to an equilibrium (by accident). Now I am wondering if and how you ...
1
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0answers
12 views

How to find covariance matrix from correlation if mean is not given?

I'm given autocorrelation function of gaussian random process: $$ R_x(\tau) = 3e^{|-\tau/3|} $$ Now I should find covariance matrix. I know the formula and solutions, where $$ C_{xx} = R - E[X]E[Y] $$ ...
2
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1answer
28 views

What was the paper about flower-shaped knots?

I read a article about the possibility to bring knots in a "polar rose" projection, where there is only one crossing of higher multiplicity. The overcrossing/ undercrossing information is thus more ...
0
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0answers
30 views

a sequence of integers associated to a bernoulli process

Is it possible to associate a sequence of integers to a Bernoulli process such that for every trial an integer is chosen and the average of the integers associated to the successes is twice the ...
0
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0answers
68 views

Confusion about a random process

Let $X(t)$ be a random process such that: $$ X(t) = \begin{cases} t & \text{with probability } \frac{1}{2} \\ 2-at & \text{with probability } \frac{1}{2} \\ \end{cases}, $$ where $a$ is a ...
1
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2answers
63 views

Random Uniformly Distributed Points in a Circle

I know that by just using a random angle and a random radius within the bounds of your circle, you will end up with points near the center of a circle. Whereas if you do ...
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1answer
92 views

Variance of a special random walk

I am trying to find the variance of the following special random walk: Suppose that $U=(U_1,U_2,...)$ is a sequence of independent random variables, each taking values $u$ (for up) and $d$ (for down) ...
1
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1answer
27 views

Suppose that $N$ is an iid geometric RV and $X_i$ is an iid Bernoulli RV. Find the p.g.f. of $R=X_1+ \dots + X_n$.

Each year a tree of a particular type flowers once and produces a random number $N$ of flowers, where $\mathbb{P}(N=n)=(1-p)p^n$, $n=0,1,2,\dots $ and $0<p<1$. Each flower has probability $1/2$ ...
0
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0answers
10 views

Clarification: Deterministic vs Pseudo- Random Number Generation

I came across the readme for a program stating that it was capable of "Simulation tooling: discrete event simulation and deterministic random number generation." I've never heard of this term used ...
1
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1answer
35 views

Continuous random variables and probability density function

OK, I know that a random variable $X$ from some probability space to $\mathbb R$, with some additional properties. It is discrete if it's image in $\mathbb R$ is dicrete. It is otherwise called ...
1
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0answers
44 views

Distinct pairs formed using repeated sequences

Problem setting: Let $N$ and $M$ be positive integers. Let $I'$ and $J'$ be ordered sets, i.e., sequences, $\{1,2,\ldots,N\}$ and $\{1,2,\ldots,M\}$ , respectively. The sequences are $N$ and $M$ in ...
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0answers
17 views

Calculation of arrival time of messages from 1 source through 2 different routes

I need to simulate sending messages from $A$ to $B$ as follows: Each message is sent $N$ times from $A$ on the same time, passes through a certain route $R_n$ and arrives at $B$. Travel time of $R_n$ ...
0
votes
1answer
143 views

Generating a random matrix with prescribed conditions

I need to uniformly generate a random matrix $X$ with positive integer entries satisfying a number of prescribed conditions: The matrix dimensions are prescribed, say $m\times n$ For each row, the ...
1
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1answer
43 views

Testing randomness

I'm looking for informations about randomness and especially - random numbers. I found some about random number generators, but for now, the question, that concerns me is how statistically differ ...
3
votes
1answer
49 views

Class of graphs with symmetric random walk

Let $(V,E)$ be a graph and let $X_n$ be a random walk on the graph. At every step, the walker at $x$ jumps to one of the neighbors drawn uniformly at random among all the vertices $y$ such that there ...
0
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1answer
22 views

Expected Value: how to understand this expression?

So I have come across a question asked by my peers. Define: $$g:=\sqrt{E[|y_r(t)|^2]}$$ Given that $$y_r(t)=\sqrt{t}\cdot h+b+k+c,$$ where $h$, $b$, $k$, and $c$ are independent random variables. ...
0
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0answers
21 views

How to compute the average power of an ergodic process?

Rxx(0)=3 is the average power and if i take limit as t goes to infinity i will get the (E[x])^2 to get variance you subtract 3-2 = 1 is this correct ? and can someone tell the difference ...
0
votes
1answer
34 views

if the probability a shooter hits the target is equal to .8 then …?

if the probability a shooter hits the target is equal to .8 then the probability that the shooter will correctly hit the target after 10 failed attempt is equal ......? probability of hitting the ...
2
votes
2answers
32 views

Expectation over multiple variable?

So I have come across a question asked by my peers. Define: $$g:=\sqrt{E[|y_r(t)|^2]}$$ Given that $$y_r(t)=\sqrt{t}\cdot h+k,$$ where $h$ and $k$ are independent random variables with variance ...