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

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-4
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1answer
37 views

probability of randomness [on hold]

If you eat three apples, two squares, and seven artichokes, what is the probability that you will become green before you become seventy. I would like real thoughtful answers. Thanks in advance.
5
votes
1answer
39 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
54 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
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0answers
20 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
26 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
29 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
11 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
52 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
22 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
85 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
19 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
29 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
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0answers
44 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
22 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
103 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
18 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
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
12 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 ...
1
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0answers
25 views

What is the deciability of randomness?

Let f(n) be a function that returns 1 iff n consecutive ...
3
votes
0answers
25 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
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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. ...
0
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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?
1
vote
2answers
41 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
28 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
107 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
185 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
20 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
29 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
30 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
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 ...
4
votes
3answers
133 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
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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
36 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
2answers
43 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. ...
0
votes
1answer
84 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?
2
votes
1answer
24 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
67 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 ...
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 ...
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
33 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 ...
2
votes
1answer
17 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, ...
0
votes
0answers
30 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 ...
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
48 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: ...
0
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0answers
20 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
82 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
26 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 ...