Questions tagged [random]

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

Filter by
Sorted by
Tagged with
5
votes
0answers
58 views

monte-carlo gone wrong

Can someone give examples where defective pseudo-random number generators gave incorrect simulation (or sampling, or polling, or gaming, …) results? I am aware of the RANDU debacle and of Ferrenberg, ...
0
votes
0answers
24 views

Are genetic algorithms mathematically sound? If not, why are they used in industry?

I was speaking to a guy with a PhD in mechanical engineering and a background in optimization and the topic of genetic algorithms came up. He dismissed them as "BS", saying that the ...
0
votes
1answer
53 views

Confusion regarding the interpretation of probability in this example

This might sound like a stupid question, but please bear with me. Suppose I have $N$ balls of different colours in a bag, and I want to know the number of blue balls. What I do is, pick up a single ...
1
vote
1answer
18 views

Random point on hypersphere surface at a uniform distance of another point on the surface

Suppose I have an n-sphere of radius 1 centered in $(0,0,...,0)$, where each point on the surface represents a multinomial distribution: Given coordinates of a point $S=(x_1, x_2,...,x_n)$ on the ...
0
votes
1answer
26 views

Is it appropriate to subtract bias when generating pseudo-random numbers?

Lets say I want to generate 10,000 random samples from a normal distribution. Is there anything wrong with first generating 10,000 numbers, then computing the mean (which will be a value close to 0) ...
0
votes
1answer
52 views

Is it possible to use one random number to derive a uniform distribution of a set of numbers?

Please imagine the following scenario: Imagine I have an indexed list of reservations, each reservation has an ID: reservations = [1,2,3,4,5] Imagine I have an ...
1
vote
0answers
53 views

Selecting a random point on a function.

Say there is a continuous function $f(x)$ which does not have any undefined points in the interval $[a,b[$. I want to randomly select a point $(x,y)$ in that interval on the line formed by that ...
-2
votes
1answer
50 views

$k\geq3$ , $np \rightarrow \infty$ show that w.h.p $G_{n,p}$ contains a copy of the k-cycle $Ck$ [closed]

I had been given this questions: Suppose that $k\geq3$ is constant and that ($np \rightarrow \infty$). show that with high probability $G_{n,p}$ contains a copy of the k-cycle $Ck$ The questions is ...
1
vote
1answer
24 views

Probability of Erdös-Renyi graph being isomorphic

Let $\mathcal{G}(n,p)$ be an Erdös renyi graph on $n$ vertices and edge probability $p$. Let $S$ be another fixed graph on $n$ vertices with $e$ edges. I am interested in the probability $$\mathbb{P}(...
0
votes
1answer
23 views

Random number generation: dealing with "change"

The goal is to generate a random integer between 1-16, inclusive, with a 6 sided die as your only source of randomness. The solution that seems to be staring me in the face is to roll three times and ...
1
vote
1answer
26 views

Generate random graphs in CSR form?

What I am trying to do is write some code to generate huge random undirected weighted graphs. I will have a parameter to control sparsity, but it will remain relatively sparse, so I want to generate ...
2
votes
1answer
62 views

n-faced dice thrown n times

We have a n-faced dice that we throw n times. p(n) is the probability to find a particular number / face. p(1) = 1 p(2) = 0.75 p(3) ~= 0.703704 For a n that reaches infinity, what is p(n) ? (To what ...
0
votes
1answer
36 views

Average time for an random-occuring occurence to occure

I've been asking myself this from a video-game that I play but I don't know how to solve it. A "monster" has 50% chance of "respawning" every 5 minutes after it's been killed. So ...
3
votes
1answer
31 views

How to explain or name 'uniform' density over a certain coordinate system?

I'm having trouble putting words on a concept. I'm comparing some Monte-Carlo data with uniformly random distributed data. The random data is not uniform in a normal rectangular coordinate system, but ...
1
vote
0answers
7 views

Expected value of first duplication by sampling elements with replacement

Let $G$ be a group of order $m$. I am sampling elements $a_1, a_2, \ldots$ from $G$ with replacement - random and evenly distributed. The question is, when will there be the first duplicate, i.e. the ...
1
vote
1answer
34 views

Moments of number of fixed points in Ewens permutations

In Ewens permutations a permutation of the first $n$ integers, $\pi : \{1, \ldots, n\} \mapsto \{1, \ldots, n\}$, is drawn at random with probability, $$ P(\pi) = \frac{\alpha^{L(\pi)}}{Z_{\alpha, n}} ...
0
votes
1answer
46 views

Expected value of random matrix multiplication

Let $\bf{A}\in \mathcal{C}^{M\times N}$ and $\bf{B}\in \mathcal{C}^{N\times T}$ be independent random matrices where their entries are drawn from complex Gaussian distributions of $\mathcal{CN}(0, \xi^...
2
votes
1answer
65 views

How do I randomly choose a number in a smaller range than what my random number generator produces?

My uniform random number generator can only produce integers in the range $0 \leq n \leq 255$. I need to use the output from this random number generator to generate another uniformly random integer ...
0
votes
0answers
12 views

Expected cycle length in random set

We know that expected cycle size of a random element in random permutation is $\frac {n+1}{2}$: https://en.wikipedia.org/wiki/Random_permutation_statistics#Expected_cycle_size_of_a_random_element But ...
0
votes
1answer
32 views

Looking for pseudo random / iterative function that generates similar numbers for similar seeds

I am writing some code to generate 2D polygonal creatures based on 2 arguments: number of edges and a seed. Using the seed and the iterative function, i generate a sequence of radius which defines the ...
0
votes
1answer
117 views

Tossing a coin infinite times

Suppose we have a fair coin. We are going to define an experiment. A single coin is tossed infinite times. Now, imagine it this way - if a coin is tossed $n$ times, the probability of getting $\frac{n}...
0
votes
0answers
22 views

Matlab probability converge

I have a homework problem ask me to use Monte Carlo simulations to validate the formulas, but I tried an easy example if I have a random variable uniformly in $[0,1]$, and I rand(n,1), with n ...
1
vote
0answers
22 views

How can I run a hypothesis test to check that a playlist shuffle is working properly?

Let's say I want to run a hypothesis test for my Apple Music playlist. Let's pretend my playlist has 50 songs for simplicity. It seems there are two conditions to satisfy: The probability of any song ...
0
votes
0answers
22 views

What is the covariance of two absolute differences between three independent random variables?

I am trying to compute the covariance between two absolute differences between 3 i.i.d Gaussian random variables: $Cov(|X_1-X_2|, |X_1-X_3|)$, where $X_1, X_2, X_3\sim N(\mu, \sigma^2)$. Since $|X_i-...
1
vote
0answers
30 views

proving $L^p$ as a normed vector space for $p > 1$. [duplicate]

I know that to prove a vector space is a normed vector space we need to prove the homogeneity, point separation and sub-additivity of the vector space. I am able to prove it for $p = 1$ (a trivial ...
1
vote
1answer
30 views

Bernoulli Sequence in Context of Random Processes

I read the following text in one of the book on Random Processes, but I am not able to understand the complete meaning of it. Consider a sample space ${\{H,T}\}^{\mathbb N}$. We define a mapping $X:\...
0
votes
0answers
10 views

If elements in matrix W are drawn from a joint continuous distribution, what can we tell about $W^T W$?

In particular, are elements in $W^T W$ are drawn from a joint continuous distribution as well? In an extreme case where matrix $W$ reduces to a scale $x$, then the answer is yes. But I couldn't get my ...
1
vote
0answers
24 views

Non-iterative deterministic function to map an input to a random output in range without repeating

Apologies if this has been answered before or is impossible, but: Is there a state-independent, non-iterative function that, given an (integer) input (n) and (integer) minimum (min) and maximum (max) ...
1
vote
1answer
55 views

Lottery fairness problem [closed]

I'm wondering if this scheme is fair or not. I'm not an expert in math so I have no clue. When lottery room starts the winning number is set by random integer between 0-999. Every player enters the ...
0
votes
1answer
32 views

Is the density a continuous function?

Let $X$ be a continuous random variable with density $$f_X(x)=x^2 I_{(0,1]}(x)+\left(\frac{7}{4}-\frac{3}{4}x\right)I_{(1,7/3)}(x)$$ The density function is $(A) \text{ right constant, but not ...
0
votes
0answers
45 views

Random permutation matrix mathematical notation

My doubt is about how could I represent this function: randperm (N, M) from MATLAB/GNU Octave or np.random.permutation from ...
0
votes
0answers
26 views

How to find the inverse/reverse implementation of a function in theory?

I have this concrete problem of reversing a function implementation: How to reverse this random number from a sequence generator function? But what I'm wondering for this question right here is, what ...
0
votes
0answers
35 views

How to reverse this random number from a sequence generator function?

I have this function, coming from this idea, to generate what feels like a random number. ...
0
votes
1answer
64 views

Does the average of random numbers in [0,1] converge?

(sorry if this is obvious or it has already been answered) If you generate a lot of random (uniformly distributed) values between 0 and 1 and take the average, the answer gets closer and closer to 0.5....
1
vote
2answers
96 views

Number of fixed points in permutations with Ewen distribution

Let $S_n$ be the set of permutations of the first $n$ integers. Draw at random an element $\pi \in S_n$ with probability $$ P(\pi) = \frac{1}{Z_{N,n}}N^{\mathcal{L}(\pi)}, $$ where $\mathcal{L}(\pi)$ ...
0
votes
1answer
27 views

Is $\frac{S_n-nE(X_1)}{\sqrt{n Var(X_1)}}$ a standardized random variable?

I want to know if this statement is true or false. The random variables $X_1,X_2,X_3,...$ fulfil the requirements of the central limit theorem. Let $S_n = \sum_{i=1}^n X_i$. Then $$\frac{S_n-nE(X_1)}{\...
0
votes
1answer
16 views

Is there a flaw with generating random percentage values and then checking the percentage?

I am developing a game project, where I have to make a lot of decisions in the form: "Place object X?". I want to say yes in Y% of the events, where I specify Y as a constant. I am using a ...
2
votes
1answer
31 views

Non-comparison based sorting algorithm based on "Number of unique integer in random generated arrays"

I have asked questions about Number of unique integer in randomly generated arrays. Suppose we have $10^6$ random generated numbers, we should have about $~6*10^5$ unique numbers. I wrote a custom ...
1
vote
1answer
72 views

Number of unique integer in random generated arrays [duplicate]

I generated 1.000.000 random integers in the range from 0 to 1.000.000 (using rand() in c++ and random.randrange() in python) and both code got approximately 632000 ...
0
votes
1answer
106 views

Can we generate the ratio of two unknown probabilities?

Suppose we have two coins $A$ and $B$, where coin $A$ comes heads up with unknown probability $p_A(0<p_A<1)$, and coin $B$ comes heads up with probability $p_B(0<p_B<1)$, and we would like ...
1
vote
0answers
48 views

Is the least-significant bit of $x_{i+1} = \lfloor 3(x_i+1)/2\rfloor$ uniformly distributed?

Consider the following simple recursion: \begin{align*} x_0 &= 0\\ x_{i+1} &= \left\lfloor \frac{3(x_i+1)}{2}\right \rfloor \end{align*} and form a string $s$ from the least-significant bits ...
0
votes
0answers
10 views

Can a Sobol sequence produce identical samples?

A recent change to the python package SAlib (used for uncertainty and sensitivity analysis) resulted in the sampling algorithm for the Sobol sequence to produce identical samples. My question is ...
0
votes
2answers
73 views

Drawing balls from a bag (Permutations).

Question: " You have $3$ green balls, $1$ purple ball and $4$ red balls, all in a bag. What is the probability that when you (without replacement) draw $4$ balls, $3$ of them will be green and ...
0
votes
1answer
35 views

Errors up to Gilbert - Varshamov bound

The Gilbert-Varshamov distance $GV(n,k)$ for binary linear code is given by the smallest integer $d$ such that $\sum_{i=0}^{d-1} \tbinom{n}{i} \geq 2^{n-k}$. Reference. If the weight of error $w$ ...
3
votes
0answers
52 views

How to logically justify the rejection of null hypothesis?

The rejection of null hypothesis will be valid only if this is true: If the probability of the obtained result given that an assumption is true is very low, then the probability that the assumption is ...
0
votes
0answers
13 views

Algorithm: Randomize Brightness and Contrast Values, With Constraints

I want to do a random brightness and contrast adjustment to an image, such that... ...
0
votes
0answers
20 views

Calculate safe amount of items for weighted random picks

Say I want to create lootboxes of 5 random items, weighted by rarity: common, rare, epic. Given I've got 10 unique common items, 6 rare items and 3 epic with weights: 0.7 (common), 0.2 (rare) and 0.1 (...
0
votes
1answer
50 views

Covariance of the sum of two random vectors

This is the situation. I have an estimation of the position $(x_t,y_t)$ of an object with its covariance $\Sigma_p$ and an estimation of its speed $(v_x, v_y)$ with its covariance $\Sigma_v$. Actually,...
4
votes
2answers
80 views

Given $2^k$ random binary sequences of length $k$, how many are expected to be distinct?

For example, say you get a uniformly random batch of $256$ sequences of $8$ bits each, and count the number of distinct sequences (i.e. discard duplicates then count), and repeat this experiment ...
0
votes
1answer
46 views

Replacing half of the content of a bottle with salt

Imagine that we have $s_0$ grams of sugar in a bottle. Then we randomly extract half of the content of the Bottle and replace it with salt. Let $s_n$ be the grams of sugar inside the bottle after we ...

1
2 3 4 5
34