# Tagged Questions

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

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?
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 (...
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 ...
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 ...
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 ...
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 ...
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 ...
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)?
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 $5$ ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $Y = \sum_i x_i y_i$. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $\alpha_0$....
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 ...
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 ...
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 ...
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 ...
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" ...
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 $g:R^2\rightarrow R$....
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 ...
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/...
46 views

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% ...
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 ...
18 views

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....