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

learn more… | top users | synonyms

0
votes
0answers
18 views

Mean time for the renewal process

The system is as below. Energy keeps coming at a node with a constant rate ρ. Node has files of size exponential(λ) to be transmitted (with fixed rate of transmission $r$, time for transmission would ...
0
votes
0answers
39 views

Presentation of 2 images in a random but counterbalanced way

Problem: For 18 trials randomly a ‘left’ labeled image or ‘right’ labeled image is shown. The first 9 trials should contain the opposite number of left images as the last 9 (a.k.a. counterbalance). ...
3
votes
0answers
39 views
+50

Arithmetic background of this RNG code

I am trying to figure out the mathematical background of the random number generation of an old video game. It does iterations where it updates a 33-bit state consisting of the variables z (32-bit) ...
1
vote
1answer
19 views

Probability and combining random variables

Adrian cycles to school with a mean time of 20 minutes and a standard deviation of 5 minutes. Pamela walks to school with a mean time of 30 minutes and a standard deviation of 2 minutes. They each ...
0
votes
0answers
17 views

Is there a such thing as a quasi-random shuffle?

I've recently experimented with Quasi-random numbers in monte-carlo applications. Is there a way to construct a quasi-random shuffle? By that I mean can I take a sequence $Q$ and shuffle it to produce ...
1
vote
0answers
7 views

Integration of a Random Process

Let {$X_t$} be a strictly stationary random process defined for all time $t$; in particular, the distribution (PDF) at any time is the same. Let $Y$ be a random variable defined by $Y = \int_0^5X_t ...
1
vote
0answers
10 views

Even dirstibution of a small set of random choices into a small set of buckets

Is there a way to evenly distribute randomly selected small set of items from a relatively larger set into to a small number of buckets using a hash function? For ex: Randomly select 20 numbers from ...
0
votes
1answer
11 views

relationship between two normally distributed variables

Say I have two normally distributed independent random variables (X1 and X2) with the same variance but different means. How would I calculate P(X1 > X2)?
0
votes
1answer
22 views

Select K numbers from N numbers fairly

I want to fairly select K numbers out of an array of N number. I know that this problem can be solved using Reservoir Sampling but I want to know if this approach is correct too? ...
0
votes
0answers
11 views

How to generate a random number according to a user defined distribution.

Assume we have a user defined distribution as following: $Q(d)=\intop_{d-\frac{1}{2}}^{d+\frac{1}{2}}G(t,\mu,\sigma)dt$ Where G is Gaussian distribution with mean $\mu$ and variance $\sigma^2$. How ...
0
votes
0answers
6 views

Stochastic Process with mean reverting property

Here I am seeking for a definition of what kind of stochastic processes are called mean reverting stochastic process. That is, what are the properties that a stochastic process should obey in order to ...
0
votes
1answer
82 views

$\pi$ normal to the base $10$ [closed]

If $\pi$ is normal to base $10$, why would we expect to find a string of ten $0$'s in its decimal expansion?
1
vote
0answers
23 views

What is the deciability of randomness?

Let f(n) be a function that returns 1 iff n consecutive ...
3
votes
1answer
481 views

Mapping random points on a sphere onto a uniform grid

Say I had an arbitrary sphere that is covered in a uniform triangle mesh of N elements with each element having a unique sequential index. If given the coordinates of a random point on the surface of ...
3
votes
0answers
23 views

Random Sampling of vectors on the Complex Unit Sphere

This is my first post in these forums. Working in Mathematica, I would like to generate a large number (10000) of randomly sampled vectors on the complex unit sphere in n dimensions. I am not ...
2
votes
2answers
829 views

What does relaxing the iid assumptions mean? Intuitive and technical perspectives.

I believe the most restrictive assumption we can place on a series of observations is that they are iid. It is possible to relax these assumptions. For example relaxing the independent distribution ...
0
votes
0answers
14 views

Randomness of a Sample

While studying about Sampling I went through a question in Data Collection. QUESTION Suppose your population is numbered 000 to 299. Use the random digit sheet by taking consecutive three digits. ...
12
votes
1answer
332 views

Does $\pi$ satisfy the law of the iterated logarithm?

It is widely conjectured that $\pi$ is normal in base $2$. But what about the law of the iterated logarithm? Namely, if $x_n$ is the $n$th binary digit of $\pi$, does it seem likely (from ...
17
votes
3answers
965 views

Are primes randomly distributed?

There is a famous citation that says "It is evident that the primes are randomly distributed but, unfortunately, we don't know what 'random' means." R. C. Vaughan (February 1990) I have this very ...
0
votes
1answer
18 views

Probability and random number [closed]

If F() generates 0 or 1 with probability 1/2 each, how can we generate 0-7 with equal probability?
0
votes
1answer
182 views

Random digits of $\pi$ seem somewhat predictable! Why is this not generally believed? [closed]

I decided to test my theory that I can guess the next digit of $\pi$ with greater than $10$% ($1$ out of $10$) confidence based alone on knowledge of previous digits. I just used a simple spreadsheet ...
1
vote
2answers
35 views

Picking 3 random books probability problem

So the question is: Suppose a bookcase holds 6 chemistry, 5 math, 3 physics, and 8 computer science texts. if 3 books are selected, find the probability that none of the math texts are selected. My ...
1
vote
1answer
27 views

Iterated uniform random variables

Define a sequence of r.v.'s {$X_n$}$_{n\ge 1}$ iteratively, such that $X_1\sim\text{Unif}(0,1]$ and $X_{n+1}\sim\text{Unif}(0,X_n]$. Could someone please explain why this is equivalent to: Let a ...
3
votes
3answers
106 views

What is the probability of getting the exact number of expected digits ($0-9$) in $10^6$ digits of $\pi$?

I noticed that at $1$ million digits of $\pi$, none of the digits has the "perfect" expected $100{,}000$ occurrences. My question is what is the probability (if the digits are truly random) of at ...
1
vote
1answer
18 views

Random number generation in MATLAB with condition

How can I generate random numbers in MATLAB with the condition that each new number has a minimum difference with all previously generated numbers for that matrix. So, X = rand(1,20) would generate 20 ...
1
vote
1answer
28 views

Flipping coin(s) to decide who pays the bill

I'm not from a mathematical background. I found this video on YouTube rather confusing. I know basics of probability from school. My question: If a single coin is flipped among 3 people say A, B and C ...
0
votes
1answer
29 views

Probability of coin flip betting

Imagine a situation where you and a friend both have 5 dollars, and you play him in a 50/50 coin flip "duel" where if it flips heads you receive a dollar from them otherwise you lose a dollar to the ...
2
votes
2answers
42 views

Is there some predictability in (pseudo-)randomness?

I was wondering if random numbers actually do have some predictability. For example, the digits of $ \pi$ are supposedly random. However, the frequency of some digits "lags" that of other digits. ...
2
votes
1answer
58 views

Good ways to sample $n$ identical and dependent random variables

I'm wondering if there's a good way to talk about sampling identical but dependent random variables where it's also easy to see how the distribution evolves as we move from $n$ random variables to ...
4
votes
3answers
120 views

What is in clear mathematical terms the definition for a sequence of integers, to be called *random*?

Sequences of integers might be ordered, totally ordered,... For all such attributes we find definitions in clear mathematical terms. (1) But what is in clear mathematical terms the established and ...
0
votes
1answer
24 views

Binomial cumulative probability

Here is the question I need help on : Let $X$ be a binomial random variable with p = 0.5 and n = 100. Give $P(X \geq 60)$ rounded to two decimal places without using a calculator (by using ...
0
votes
0answers
18 views

Sampling from a random distribution with a margin of error

A survey of a population is taken using sampling. It is determined that 70% prefer option A and 30% prefer option B with a margin of error being 5%. Typically when simulating the process with the ...
2
votes
2answers
33 views

What is the mathematical notation for a random number in a certain range?

In school, I was taught to denote a random variable like so: $$R=\{_{0}^{1}$$ This only goes for a random choice between two integers, like a coin flip. How do I write a variable that is equal to a ...
2
votes
1answer
21 views

Can a collection of random processes be not random?

A friend and I were having a debate about randomness and at one point, I said that it was possible to have a collection of random processes which were not random when "put together." He disagreed. ...
1
vote
2answers
52 views

generate random number from exponential distribution with random right truncation

I need to draw a random number from an exponential distribution (rate $mu$) that is right-truncated with the truncation value coming from a gamma distribution (shape $k$, rate $lambda$). My naive ...
0
votes
0answers
20 views

Probabilistic Method in language membership decision

$F(x,r)$ is a random algorithm to decide membership of input $x \in \{0,1\}^n$ to a language $L$. $r \in \{0,1\}^n$ is randomly selected bits. We know the if indeed $x \in L$, then the probability ...
0
votes
1answer
31 views

Expected value of a sum of random events

Suppose there's a market that has decided to award its most loyal customers. The market sells a certain type of breakfast cereals with a single token in each box. There are n different types of ...
0
votes
0answers
25 views

Gaussian random processes

Let A B and C be Gaussian processes. If A&B are jointly Gaussian, and B&C are jointly Gaussian then A and C are jointly Gaussian? Is this statement true? and can it proven? (or any ...
2
votes
1answer
16 views

Can I use one float random number to generate two random numbers, one discrete, one continuous?

I need two random numbers. The first one, u, is discrete and takes 70% of the time the value 0 and 30% of the time the value 1. The second one, v, is continuous and takes values uniformly inside [0, ...
1
vote
2answers
348 views

Simple algorithm for generating Poisson distribution

I found a very simple algorithm that draws values from a Poisson distribution from this project. The algorithm's code in Java is: ...
0
votes
0answers
12 views

Will XORing any data with random data produce a random result?

Provided you have a stream of input data and a stream of random data both in the set (0,1). The random is data truly random, that is, unpredictable by the user and ...
0
votes
3answers
46 views

Generate random number with specific probability distribution

Well consider I have a uniform random number generator. How would I craft a function which takes as parameter this RNG, such that the distribution is following a given function? Or more to the point: ...
5
votes
2answers
977 views
3
votes
2answers
625 views

Random Variable Probability Russian Roulette

I am very confused on this one. Any help in how to solve it and what probability rule to use would be appreciated. Consider the situation in which a person played Russian roulette (one bullet, 6 ...
5
votes
0answers
141 views

Random 3D points uniformly distributed on an ellipse shaped window of a sphere

How can I generate random points uniformly distributed on the surface of a sphere such that a line that originates at the center of the sphere, and passes through one of the points, will intersect a ...
1
vote
1answer
18 views

Random conversions

I came across a question in StackOverflow which states the following, all is based on natural numbers: Given the function rand5 (which produces random natural numbers 0-4), use it to generate a rand7 ...
0
votes
0answers
18 views

Increasing the speed of a depth first search.

I am looking for ways to increase the speed of a depth first on a graph when trying to find a path from a source node to a destination node. One thing I have tried is to perform a bidirectional ...
2
votes
2answers
77 views

Probability a product of $n$ randomly chosen numbers from 1-9 is divisible by 10.

I'm working on a problem where each number is chosen randomly from 1-9. Given $n$ numbers chosen in this manner, we multiply all of these together. I'm looking for the probability that this product is ...
0
votes
0answers
25 views

Divergence of series

Given that a is a non 0 real number and ck is a series of real number for all k natural number where $\sum_{k= 1}^{\infty} c_k^2 = \infty $. If $c_k \to 0$, proof that $lim _{n \to ...
3
votes
1answer
20 views

Distribution of numbers $n = \max(x, y)$ where $x, y$ are random numbers between $0$ and $1$

I define a function $$f = \max(\mbox{rand}(0, 1), \mbox{rand}(0, 1))$$ such that $f$ returns the maximum (greater number) of two random selected numbers between $0$ and $1$. Plotting a histogram for ...