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

learn more… | top users | synonyms

0
votes
1answer
18 views

Multiple rolls of a one hundreded sided dice

Let's side I have a one hundred sided dice and a friend picks 8 random numbers from the dice. I understand that if I roll the dice one time, he has an 8% chance of getting the roll correct. My ...
-3
votes
0answers
16 views

Probability 2 balls in a bag [on hold]

consider an experience which consisit of drawing 2 balls with replacement from an urn containing 7 balls of which 3 are blue and 4 are yellow (i)what is the sample space (ii)define the events as a ...
-1
votes
1answer
17 views

is it possible to implement random(0,1,..,m) with finite calls to random(0,1)? [closed]

that is, is there a function $f$ that $Y=f(m,X_1,X_2,...,X_{n(m)})$ where $X_i\sim B(1,\frac{1}{2})$ and $Y\sim U\{0,m\}$? e.g. when $m=2^k-1$,$n(m)=k$ and ...
2
votes
0answers
12 views

Random allocation of groups of objects to agents

I have a poorly specified random allocation problem, which I need help in trying to tighten the definition and consider an effective algorithm. I have groups of objects, each group containing at ...
0
votes
0answers
13 views

K-Uniformity of Infinite Sequence

A book on random number generators refers to the subject of infinite-uniform infinite sequences as being "random." I was wondering if anyone could shed light on the definition of K-Uniform Infinite ...
1
vote
0answers
22 views

Probability that an individual cheated and knows a random sequence.

Bob writes down a sequence of coin flips on a piece of paper and hides it away. He uses a coin flip to determine if he uses a 1 or a 0. Alice tries to guess the random sequence and may have looked at ...
0
votes
2answers
20 views

Deriving probability densitys

How does one derive probability densitys involving fractions? For example, let $X^2$ and $Y^2$ be exponentially distributed random variables with parameter $\lambda = 1$. Determine the PDF for $Z = ...
0
votes
0answers
12 views

Deterministic seeded shuffle

How can I find an injective function $f$ so that mapping that function over each element of the ordered sequence $[1\cdots{n}]$, yields a deterministic shuffle (random permutation) that is "good" ...
-1
votes
0answers
18 views

Rayleigh Quotient

I have two questions: 1) suppose $w \in C^{N}$ is a size-N unit-norm complex random vector, and it is independent and identically distributed with a uniform distribution on the sphere. I would like ...
0
votes
1answer
34 views

What's duplication probability of the next discrete random number?

If I already have n random numbers(between 0-100), what's the duplication probability when I random next number? This is a chart represent probability(0-100%) of this question when n is between ...
1
vote
4answers
71 views

What would be the maximum number of guesses for a random number between 1 and 9?

How many guesses could someone get wrong if they were trying to guess a number between 1 and 9, with the integer always changing with each attempt? For example: If a random number generator had ...
2
votes
1answer
43 views

What is a thorough method to manually generate a random number between 1 and 100?

The other day, I got an idea. I would like to generate a random number between 1 and 100 , however by hand. And only using simple tools like a desk clock and pen and paper. What might be a way to do ...
0
votes
1answer
17 views

Blum Blum Shub pseudorandom numbers - clarification on prerequisites

By reading on Wikipedia, they say the following (these is also supported by the following work: http://www.daimi.au.dk/~mg/mamian/random-bits.pdf) The seed x0 should be an integer that is co-prime to ...
1
vote
0answers
45 views

How can non-binary data be tested for distinguishability from random?

Given a large string of Base-N digits (in other words, not necessarily binary), is there software or an algorithm that can output whether the data is reasonably pseudorandom or reveals a pattern? In ...
16
votes
1answer
236 views

Flaw or not flaw in Excel's RNG?

I have a question about my understanding of an article of B.D. McCullough (2008) about Excel's implementation of the Wichmann-Hill random number generator (1982). First, a bit of context The ...
0
votes
0answers
28 views

Random Matrix Theory Noise

Hello and Merry (past) Christmas! I am new to random matrix theory, was reading an article about how to improve a correlation matrix (for portfolio optimization). And everywhere i see this "noise ...
0
votes
0answers
45 views

What is the chances of a duplicate in this equation [duplicate]

I'm not very good at math; However I have a scenario where I'm trying to find the chance of duplicate for randomly generated data. In a nuttshell I have a "bag" with 62 different items, lets say a ...
5
votes
1answer
53 views

Choosing primes uniformly at random

I'm interested in efficient methods of generating prime numbers in a given range [a, b] (or with a given number of bits/digits, etc.). By "efficient" I mean minimizing time, randomness, and perhaps ...
1
vote
1answer
63 views

Proofs involving positive real numbers

I have two questions related to positive real numbers: If a and b are two vectors of positive random integers (no specific statistical distribution) and size N by 1 , we want to prove that the inner ...
0
votes
0answers
33 views

Randomness of a linear congruential genarator

I am working on a school project and it requires a simple pseudo-random number generator. I thought of using a linear congruential generator for this purpose. Here's a link ...
0
votes
0answers
29 views

Probability distribution of the upper limit of an RNG given finite set of results

Suppose an unweighted random number generator outputs a random integer in the range $[0,u]$, and suppose I generate $n$ numbers and store the maximum number generated, $m$. Given only $m$ and $n$, can ...
1
vote
1answer
33 views

Can you select random entry from unknown number of entries?

Imagine you've got entries coming in, without knowing when they end (how many will follow from now on). You're supposed to pick random one and be fair. You can't save the entries that passed but you ...
1
vote
1answer
15 views

Application of Borel-Cantelli for sequence of two parameters

Let $(A_{m,\ell})_{\ell \geq 0, m \geq 0}$ be a sequence of events in some probability space. How to show by using Borel Cantelli that, if $$\sum_{\ell \geq 0, m \geq 0} P(A_{m,\ell}) < \infty,$$ ...
0
votes
2answers
57 views

Expected Value Of a Random Variable X

Consider an experiment that is successful with probability $0.8$. We repeat this experiment (independently) until it is successful for the first time. The first $5$ times we do the experiment, we ...
0
votes
0answers
24 views

How to find the right way to pick a random selection

I love the website AnyDice (http://anydice.com). When I needed to make a dice game, it saved me hours of coding and testing. Now, I need something similar, but not for dice. I'm trying to do a ...
1
vote
4answers
92 views

Expected value of a run of a random bitstring

A maximal run of ones in a bitstring is a maximal consecutive substring of ones. For example, the bitstring $1000111110100111$ has four maximal runs of ones: $1, 11111, 1,$ and $111$. ...
0
votes
0answers
21 views

How to generate random numbers when given the value of a probability density function?

When given a set of values deriving from a probability density function f, like this {f(X1),f(X2)... f(Xn)} But we don't know the exactly form of f.Is it possible to project it to a closest ...
0
votes
0answers
32 views

Mean time for the renewal process

The system is as below. The energy arrival process is $Y_{k}$ with a constant rate of $\rho$. Node has files of size exponential(λ) to be transmitted with fixed rate of transmission $r$. Hence the ...
0
votes
0answers
48 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). ...
1
vote
1answer
25 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 ...
7
votes
1answer
108 views

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) ...
0
votes
0answers
20 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
12 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
20 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
25 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
7 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 ...
1
vote
0answers
25 views

What is the deciability of randomness?

Let f(n) be a function that returns 1 iff n consecutive ...
3
votes
0answers
33 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 ...
0
votes
0answers
17 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. ...
0
votes
1answer
19 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?
1
vote
2answers
45 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
31 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
108 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 ...
0
votes
1answer
201 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
1answer
26 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
31 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
39 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 ...
0
votes
1answer
26 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 ...
4
votes
3answers
149 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
0answers
19 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 ...