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

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6
votes
3answers
720 views

Is it necessary that if a limit exists at a point it should be also defined at that point?

Say there exists a limit $\lim_{x \to x_0}f(x) = L$. Is it necessary that $f$ be defined at the point $x_0$ itself? Well, what I think of it is that it's OK to be undefined at that point because I ...
1
vote
1answer
26 views

Mistake in generating random numbers - no irrational ones

Hi I just wondered if the probability densities have to be corrected when using them on a PC since the number representation is not at all continuous. So we cant simulate any irrational numbers and ...
0
votes
0answers
7 views

unltra-simplistic linear congruential random number generators

The real linear congruential number generators are more complicated but it is possible to generate a sequence that hits every number in 32 bits using only: ...
0
votes
1answer
29 views

Total possible Combinations

I have a quick question. I'm terrible at math so when I read the other posts on this it made no sense to me. I'm creating a trading card game, and I need to know how many possible UNIQUE cards my card ...
0
votes
0answers
24 views

Mean absolute distance for a symmetric random walk

I have found that the mean absolute distance for a symmetric random walk after n steps can be computed using this product: What can be deduced from this? For example how can variance be computed ...
0
votes
3answers
40 views

Probability of card color

Task: In box are three cards. First card is red on both sides. Second card is black on both sides. Third card is red on one side and black on other side. I random choose one card and I see that ...
1
vote
1answer
32 views

Generating random groups satisfying certain conditions

I am trying to find a counterexample to a claim about groups. I need a random generator (a program in any programming language, or an algorithm) which will generate a random group $G$ of any order ...
1
vote
0answers
26 views

Prove the bounds on expected value of minimum distance

Let $X_1,X_2,...,X_n$ be $n$ i.i.d. samples from the uniform distribution on the unit square $[0,1]^2$, and let $x \in [0,1]^2$ be an arbitrary fixed point. Prove that there exists some constants ...
0
votes
0answers
28 views

Does Chaitin's constant mean true randomness exists?

I've been reading about Chatin's Constant, and some of the information there seems to contradict what I've heard before. It says that the digits of Chatin's Constant can not be computed. This means ...
1
vote
1answer
19 views

Is an event with a fixed number of outcomes considered random if one outcome is more likely than another?

My friend says that even though an event has (for example) three outcomes with outcome A at 10 percent, outcome B at 10 percent, and outcome C at 80 percent that the outcome of the event is still ...
1
vote
1answer
18 views

The rand function/algorithm - when does it begin to develop a pattern?

this question is rather general but I am sure a specific answerer or at-least a theoretical answerer can be provided on it. The rand function is a random number generator that runs on a seemingly ...
1
vote
0answers
36 views

Joint probability density function of two dependent gaussian variables

I have faced the following dilemma while doing some research, so your kind support will be highly appreciated. I have the following two random variables: $$X_1 \sim N(\mu_1,\sigma^2_1)$$ $$X_2\sim ...
1
vote
0answers
25 views

What does it mean that a Monte Carlo (MC) algorithm is correct with probability at least $p$?

I was trying to understand the definition of what it meant to say that a Monte Carlo (MC) algorithm succeeds with probability at least $p$. Usually in probability I would have concluded that the ...
1
vote
1answer
26 views

Expected value related to Brownian motion

Suppose $\{W_t:t \geq 0\}$ is a Brownian motion, let $0 \leq s<t$, what's the following expected value: $\mathbb{E}[W_t^3-W_s^3-3(tW_t-sW_s)]$ $\mathbb{E}[W_t^4-W_s^4-6(t-s)W_s^2-3(t-s)^2]$. ...
0
votes
0answers
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?
0
votes
0answers
11 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 ...
0
votes
1answer
40 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 ...
0
votes
0answers
28 views

How many random points so i need to pick such that I can truly represent the dataset I am sampling from?

How many random points do I need to select to truly represent a set of points? I have around 750 points in my dataset and I'm currently randomly selecting 300 points. I know the dataset is not large ...
1
vote
1answer
53 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 ...
1
vote
0answers
21 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 ...
0
votes
0answers
14 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 ...
1
vote
0answers
14 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 ...
0
votes
0answers
40 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)?
0
votes
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 $5$ ...
1
vote
2answers
101 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 ...
1
vote
1answer
54 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 ...
0
votes
1answer
26 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 ...
0
votes
1answer
26 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 ...
1
vote
0answers
16 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 ...
3
votes
0answers
40 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 ...
0
votes
0answers
22 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 $Y = \sum_i x_i y_i$. ...
1
vote
0answers
40 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 ...
1
vote
1answer
28 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 ...
0
votes
1answer
44 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 ...
2
votes
2answers
33 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 ...
1
vote
2answers
82 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 ...
1
vote
1answer
40 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 ...
1
vote
1answer
57 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 ...
0
votes
1answer
48 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 ...
0
votes
1answer
33 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 ...
0
votes
0answers
15 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 ...
1
vote
0answers
73 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" ...
-1
votes
1answer
58 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 ...
0
votes
4answers
175 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 ...
0
votes
0answers
43 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 ...
1
vote
0answers
45 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 ...
3
votes
3answers
64 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 ...
1
vote
0answers
29 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 ...
0
votes
1answer
40 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% ...
1
vote
2answers
33 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 ...