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

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26 views

What class of probability distributions do probabilistic turing machines induce?

What class of probability distributions is induced by the class of probabilistic turing machines? Is there a precise characterization?
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13 views

How to generate X random winners from a lottery for a given period of time?

I need to determine lottery winners in the following game-type setting: You can register in the lottery with your unique id (let's say your email address) which means that you can register only once (...
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1answer
73 views

Can we draw the graph of the derivative/integral of a function by using the graph of the function only?

Consider a function say $F(x) = x^2 + 5\sin x$ then we have it's derivative as $F'(x) = 2x + 5\cos x$ and thus we have the graph of $F'(x)$ quiet easily but can we plot a graph using only the graph of ...
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1answer
57 views

Random walk - Markov chain

I have a problem.If we start at place $0$ and the probability to go right is $p$ and the probability to go left $q$. I need to calculate the probability after 100 steps that the maximum place when we ...
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0answers
26 views

rms width calculation

I have a Equation with following form: $$v(t)=e^{-( t/T_0 )^2}\sum_{n=-N}^{n=N}C_nCos(n\Omega t)$$ where $C_n $ is uniform random variable that take two integer 1 or -1 ,and $\Omega ,T_0, N $ are ...
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0answers
20 views

Generating a sequence of random numbers as a random seed for gambling

We have a simple game where a player wins if a random number is greater than some threshold (say 0.5 on 0-1 scale). The player commits to a game first, and then we generate proceed to generate the ...
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0answers
15 views

Working out the average number of selections required to select each item of a list at least once when using random selection with replacement?

So, most combinatorics I've looked at while researching this consist of limiting the number of selections made from a set X and working out the probability of a particular combination of results. In ...
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0answers
135 views

product of two chi-squared distributed variables

What is the expected value of the product of two chi-squared distributed variables (E[XY] where X and Y are chi-squared distributed random variables)?
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1answer
14 views

Probability of choosing $x$ in a sample of $m$ choosen from the total of $n$

Sorry for being ambiguous but the question is that a class contains $25$ boys and $15$ girls.   What is the probability of choosing $5$ students at random and choosing $3$ boys? So the $5$ ...
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2answers
221 views

Statistical probabilities to win the lottery

I'm trying to figure out what is the statistical probabilities to win the lottery. Let's assume that we pick 6 numbers out of 40 so : 1/40 × 1/39 × 1/38 × 1/37 × 1/36 × 1/35 = 1/2763633600 Up until ...
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1answer
69 views

Randomic distribution

Suppose I have X elements [A,B,C,D,...] and Y subsets of X of max length 4. Suppose the subsets are build up randomly, is there a way to compute the average number of subsets an item of X is an ...
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1answer
27 views

Need way to statistic puzzle

Hello guys i need help with statistic problem. The problem is : In room have 3 doors, one door is exit from room (o minutes) , second is return us to the room after 3 minutes , and last door is ...
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1answer
30 views

Using dieharder to certify randomness of a random sequence

I would like to prove (at a certain level) the randomness of a random sequence of N bits. I know that the dieharder battery of tests is supposed to be used to test the generator, not a particular ...
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0answers
17 views

Distribution using the Poisson Point Process model

I need to use the Poisson Point Process (PPP) model to randomly distribute a set of 'objects'; over a given area: Let's say that we have N objects to distribute over an area that has been split ...
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0answers
53 views

Random Numbers and probability

How long does a sequence of random decimal digits (0, 1, 2, ..., 9) need to be before you can "reasonably" expect the sequence to contain all numbers from 0 through 999 (inclusive). -- It's up to ...
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0answers
23 views

bounding absolute fluctuations of random variable distribution

I have a discrete random variable with values $\underline{y} = (y_1, y_2, \dots , y_d)$ with corresponding probabilities $\underline{x} = (x_1, x_2, \dots , x_d)$ and average $Y = \sum_i x_i y_i$. ...
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1answer
53 views

Logic behind Metropolis algorithm

I am using Metropolis algorithm to make a program for Ising model in Statistical Physics. In Ising model, we take a collection of spins with initial energy, say $E_i$, then we randomly flip one of the ...
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1answer
29 views

Is there a way to generate this class of bivariate distributions from two uniform random variables?

I need to generate a pair of random variables $U,V$ with distribution $$ f_{U,V}(u,v)\propto(u+v)^{-4} $$ in $u,v\in[1,L]$ with $L>1$. I managed to invert the CDF of the marginal distribution for ...
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1answer
62 views

What is the difference between Discrete and Continuous Random Variables?

What is the difference between Discrete and Continuous Random Variables? Discrete Random Variable = takes countable or discretely determinable values. So, it is always listable. For example, digital ...
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2answers
45 views

Why a shuffling algorithm is not uniformly random between [1, N)? [closed]

I've been taught that simple shuffle algorithm will not be uniformly random if the interval for the random numbers is not [1, N), i.e. it can't be from 0 to N, it must be from 1 to N-1. I'm trying ...
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2answers
92 views

Continuous Random Variable question, Probability and Statistics

a little help please A couple decide they really want a daughter. So, they decide to start having children and continue until they have their first daughter. Assuming having either a boy or girl is ...
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1answer
50 views

Convergence of sequence of random variables to infinity

Suppose $X=X(\alpha)$ is a sequence of non-negative continuous random variables indexed by a continuous parameter $\alpha$ such that $\alpha$ is in $[0,\alpha_0)$ for some finite positive $\alpha_0$....
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1answer
73 views

Random but very interesting probability question! [duplicate]

There are 100 types of cards, each type with a number from 1 to 100 on it. Each minute I am given a random card. Random means that the number of my card has an equal chance of being 1,2,3,...,100. I ...
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1answer
68 views

Wiener Process definition - Continuous paths?

A stochastic process $\{W(t): t \in T\}$ is a Wiener process if it satisfies the following properties: 1) $W(0)=0$ with probability $1$ 2) It has stationary and independent increments. 3) For every ...
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1answer
50 views

How do multiple trials affect certainty?

Suppose you have two coins: one is a normal coin (with one "heads" side and one "tails" side), and the other is a modified coin with two "heads" sides. The coins are indistinguishable apart from ...
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0answers
18 views

Permutations for a linguistics project

I am going to have subjects read the following word lists: English A English B English C Spanish A Spanish B Spanish C I always want the subjects to alternate between reading English lists and ...
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0answers
115 views

Invertible pseudo random number generator

I want to create a random sequence using a given seed. However when given a sequence I also want to calculate the seed which produces the sequence. Of course this is not possible using a "true" ...
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1answer
59 views

Show that if $(X_1,Y_1)$ and $(X_2,Y_2)$ are independent random vectors, then $(X_1,Y_1,g(X_1,Y_1))$ and $(X_2,Y_2,g(X_2,Y_2))$ are as well.

I am not sure how to go about showing that $(X_1,Y_1)$ and $(X_2,Y_2)$ being iid implies that $(X_1,Y_1,g(X_1,Y_1))$ and $(X_2,Y_2,g(X_2,Y_2))$ are iid for any measurable function $g:R^2\rightarrow R$....
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4answers
298 views

Random irrational number generator?

Is it possible to create a algorithm that will generate irrational numbers $0<x<1$ with a density that is uniform down a specified resolution? Would such an algorithm be necessarily limited to ...
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0answers
64 views

How to draw lots in a group of people without duplicates and not all present

I have a problem that certainly has some mathematical solution. The problem: In a group everybody writes his/her name on a paper, puts it in a bowl and everybody draws a paper. If someone draws his/...
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0answers
46 views

How to approximate damped harmonic under random forcing

Given motion in response to random forcing, can a "simple" function be used to estimate future motion. Starting with the damped harmonic oscillator, we can write $${d^2 \over {dt^2}} h(t) + 2 \zeta \...
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3answers
86 views

Probability doubles if you switch cards when the third card is revealed, How? [duplicate]

So I was watching the show Numb3rs, and the math genius was teaching, and something he did just stumped me. He was asking his class (more specifically a student) on which of the three cards is the ...
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0answers
52 views

How to efficiently sample a point in a polyhedron

I have a polyhedron $P$ described by $$ P = \{ x | Ax \preceq b\}, $$ $x \in \mathbf{R}^{n}.$ I want to randomly generate points that are inside $P$. One way is to just generate random points and ...
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1answer
48 views

Finding the average cluster size of a random grid

Original problem statement: Melon-boy lives in a flat world, where there is an infinite two-dimensional grid, where each gridsquare is either occupied by a melon (50% chance) or a pumpkin (50% ...
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2answers
36 views

Probability of single digits from coin tosses

Let's say that I wanted to generate 4 random numbers using a coin toss. I could toss the (unbiased) coin 4 times to generate one of 16 possible numbers (e.g. TTHH=0011=3) and just ignore any results ...
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0answers
18 views

Why are the Real and Imaginary parts of a field in k-space uncorrelated?

I am in the process of generating a (real) Gaussian random field $\delta(\vec{x})$ from a given power spectrum $P(k)$. The way I define the power spectrum is, in Fourier space, $\left\langle \delta(\...
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0answers
104 views

Generating a Random Connected Graph

Given a graph G(V, E), with |V | = n and |E| = 0 (that is, the graph is empty), and a static set F containing all the possible edges. Consider the following algorithm for generating a random graph. ...
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1answer
62 views

uniform distribution vs normal distribution for discount use case [closed]

Problem statement: Reward a customer with lucky draw coupon of X% discount in between 1% to 100% Assume that slabs are pre-defined ( all are theoretical) 1% discount : 90% customers 10% ...
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1answer
57 views

LCM of randomly selected integers

What is the expected LCM of 21 randomly selected positive integers under 10000000? How would someone even approach this problem? EDIT: The positive integers are chosen with replacement.
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1answer
42 views

Is $a+r \cdot b$ an uniformly random value when $a,b$ are fixed and $r$ is random value?

Imagine we have two fixed values $a,b \in \mathbb{Z}_p$ and a uniformly random value $r\leftarrow \mathbb{Z}_p$, for large prime number $p$. Question: Is $v=a+b\cdot r$ an uniformly random value in $\...
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0answers
22 views

the meaning of 4-wise hash function

If someone says: 4-wise independent sign (hash) functions $s_1,s_2, s_3 : [d] → \{+1, −1\}$, then what does it means? I cannot use k-wise Independence variables (the definition 1 http://www.math....
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2answers
59 views

What is the probability that at least one 10 day period contains 6 birthdays if there are 60 birthdays throughout a year?

For all possible contiguous 10 day periods within a single calendar year, what is the probability that at least one of the 10 day periods contains six birthdays if there are 60 birthdays randomly ...
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1answer
53 views

Nonlinear transform of two random variables for Gaussianity

I would like to understand the nonlinear transform of Gaussian random variable that preserves Gaussianity better when there is no $x_3$ term such that there exists a nonlinear relationship between $...
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0answers
46 views

Mathematical expression for randomly selecting from two integers

I wonder what is the shortest and correct mathematical expression for the below: $x =$ random$(1$ or $2)$ where there is equal probability of selecting 1 or 2. Thanks for your help.
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29 views

mathematical notation for random selection of two integers

I want the shortest mathematical notation for the below: $x =$ random$(1,2)$ where there is equal probability of selecting 1 or 2. is it correct to state: $x \sim$ U$(\{1,2\})$. If I had more ...
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1answer
69 views

Partially Identical Hands in Hold'em

I was playing Texas Hold'em at a local cardroom last night keeping a meticulous record of the hands I was dealt. Perhaps I am totally wrong but I thought the occurrences of certain events in this ...
3
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0answers
67 views

independence of x/y and y given that x and y are not independent [closed]

Suppose two non-negative random variates x and y are NOT independent (in my case that I am interested in, the range of x is constrained by y, i.e., $0<x\leq y$). In more specific, assuming $y$ ...
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2answers
38 views

Choosing something 35% more often

If I want to select an element from an array at random, the following will choose each element roughly at 1/L percent of the time: ...
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1answer
68 views

Stat: Probability to have one element of a combination identical to one element of another combination

For a business application, I currently have to provide the probability we are going to have an issue in one application. The combination is composed of N unique ...
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1answer
51 views

Apportioning $100\%$ across $24$ hours

Assume I have value $x=500$. I would like to apportion this value $500$ across $24$ hours time period and would like it to be apportioned randomly. So if $500$ is $100\%$ the $x\%$ generated at random ...