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

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2
votes
1answer
55 views

Probability question (grid)

Say I have a grid of 10x7. Every square of that grid is empty. Then, 20 squares, chosen at random, are filled (a square can only be filled once, so no duplicates allowed). What is the probability of ...
2
votes
3answers
127 views

Probability of collecting all 5 different items at random with different weights

There are 5 different items in a set, each with a weighted chance of being rolled randomly [A-E]. The weights add up to 100%. $$A=5\%, B=10\%, C=15\%, D=30\%, E=40\%$$ You get 1 item every roll no ...
2
votes
0answers
85 views

Random pair generation?

Suppose there are 6000 people, there will be a combination of $$\binom{6000}{2}$$ ways for 2 people to be chosen out. Now the task is to randomly choose 5000 pairs of people in the total 6000 ...
0
votes
1answer
146 views

Generating Random Serialnumber with least similarity

I want to generate 16-digits hexadecimal serial-number like: F204-8BE2-17A2-CFF3. (This pattern give me 16^16 distinct serial-number But I don't need all of them as I describe below) I need an idea ...
0
votes
1answer
89 views

What is a pdf of Gaussian noise convoluted with a sine wave?

I realize that it is relatively easy to compute the variance of an AWGN convoluted with a sine-wave through auto-correlation function. My question is how do I find the pdf if I know the variance and ...
-1
votes
1answer
220 views

random number usage in filling 2d array

Below is a small program which has 2-3 Math concepts involved we have 2d array of $i$ width and $j$ height, idea of this program is to fill ...
1
vote
2answers
20 views

Show that $Cov(X,Y) \geq -23$

if $X,Y$ are two random variables and: $Var(X) = Var( Y) = 23$ how can i show that $Cov(X,Y)\geq -23$ can someone give me some hints on how to show it?(not an answer) i know that $Cov(X,Y) = E(XY) ...
1
vote
2answers
59 views

the maximum of two random variable

The maximum of two random varibles $X$ and $Y$ is: $$Z=\max\{X,Y\}= \begin{cases} X & \text{if } X \geq Y \\ Y & \text{if } Y \geq X \end{cases}$$ I don't understand. So if I roll two dice, ...
3
votes
0answers
38 views

Can I solve this probabilistic problem or do I need more data?

This problem happened to me almost 3 years ago and I just discovered this site by luck, so I want some help to know if this problem is solvable (if so, I would like to know how to solve it as well as ...
0
votes
0answers
16 views

Singular value of random matrix after linear transformation

Let $A$ a $n \times n$ random matrix with i.i.d $N(0,\sigma^2/n)$ entries. Let $H$ an invertible matrix, and denote $\sigma_H$ the largest singular value of $HAH^{-1}$. My question is : in the large ...
2
votes
2answers
234 views

Why do people say that prime numbers are “random”? [closed]

Compared to most of the people who frequent this place I suppose I am not very smart, but I do have a solid basic and somewhat intuitive understanding of mathematics. Now prime numbers have always ...
1
vote
1answer
43 views

Algorithm to generate normal matrices at random

I would like to generate normal matrices by an, say python, algorithm, that produces normal matrices distributed evenly in the limit of large n. I would not like to be restricted to Hermitian matrices ...
0
votes
2answers
57 views

Distribute a population size based on fractions using random number generator drand48()

I have a population size of say 5000 people. Every person belongs to either A, B, C or D category. I want to split the population as per a given fraction provided by user. for example, 99% of A, 0.4% ...
0
votes
1answer
21 views

Looking for a random statistical biaised function

A common random function is designed like a dice, if you call it many times it will yield approximately the same number of times 1, 2, 3, 4, 5 and 6. Statistically, you could say it's equally spread ...
0
votes
0answers
76 views

Derive c.d.f and p.d.f of a random variable which is defined as function of two random variable

Let $x_1$ and $x_2$ are independent random variable with p.d.f $f(x_1)$ and $f(x_2)$. How to derive c.d.f and p.d.f of random variable $y$, which $y = \frac{x_1 x_2}{ax_1 x_2 + bx_1 + cx_2 + d}$ ...
0
votes
1answer
69 views

2 dimensional random walk - hit of targets

Consider a random walk in $\mathbb{Z}^2$, $x(j) = x(j-1) + \xi_j$, where the increments are random variables independent and identically distributed with finite support, the expectation $m := ...
0
votes
2answers
50 views

Finding derivative of this integral function.

I need help on finding the derivative of this: $$g(x) = \int_1^{x^2} (x-t)\sin^2(t)dt$$ I thought about taking out x and having it as a constant but how?
0
votes
0answers
29 views

Spatial randomness of 2-tuples

Lets consider a sequence of 2-tuples $\{(x_i, y_i)\}_{i=1}^n$ in a bounded 2D space. My goal is to investigate the random distribution of these 2-tuples. Can I deduce the spatial randomness of ...
1
vote
1answer
3k views

'normally distributed random numbers' vs 'uniformly distributed random number'?

what is the difference between 'normally distributed random numbers' and 'uniformly distributed random number'? A answer in a layman language is appreciated :)
4
votes
0answers
63 views

Entries of a Haar distributed unitary matrix

The eigenvector matrix of a Wishart matrix is Haar distributed and that implies that the eigenvectors are uniformly distributed on a sphere. I'm interested to know what is the distribution of ...
0
votes
1answer
105 views

how to generate Normally distributed random number?

I am looking for a function that can generate Normally distributed random numbers. I came to know about bux-muller transform but I didn't understood it completely what it is doing. Thus it would be ...
1
vote
0answers
22 views

generating locally random permutations

I have an intuitive notion of 'local randomness' that I am trying to make precise and understandable, and I am running into a bunch of problems. A quick web search failed to find anything relevant in ...
0
votes
1answer
74 views

Needed a math function, Don't know what to call it?

I need a math function $f(\ell)\to n$ whose input is a list of numbers and whose output is a noisy value (random value added to original input to get noisy output). The function $f(\cdot)$ should have ...
0
votes
1answer
80 views

random walk with dependent increment

Consider the following sort of random walk. The position of the walker at time $t$ is represented by the random variable $r(t)$, with $r(0) = 0$. The variable satisfies the following equation, $$ ...
0
votes
2answers
48 views

Pseudo random ordering of integers

I remember an old retro effect for a screen resolution of $320\times 240$. You would iterate the pixels in a linear fashion so there are $76800$ pixels. You could iterate then one by one starting at ...
30
votes
3answers
4k views

Why does this not seem to be random?

I was running a procedure to be like one of those games were people try to guess a number between 1 and 100 where there are 100 people guessing.I then averaged how many different guesses there are. ...
2
votes
0answers
104 views

Using an elliptic curve to create pseudo random number

I recently started learning about encryption. I read about how elliptic curves can be used to create pseudo random numbers (and how the nsa might have abused this fact to create a backdoor in ...
4
votes
3answers
174 views

Recursion with Random number?

function foo(n) if n = 1 then return 1 else return foo(rand(1, n)) end if end function If ...
0
votes
0answers
34 views

Explicit computable discrete pseudo random walk

Is there any algorithm that would be able to explicitely calculate a value $n_i$ for any index $i$, so that the sequence $n_0,n_1,...$ could also be a realisation of some random walk?
0
votes
1answer
90 views

What is the expected error of a randomly generated number?

Forgive me if this question is unclear, as I'm not a mathematician. The question has come up in an industrial sensor application. I am trying to make the displayed sensor value to be more steady ...
4
votes
3answers
224 views

Probability that a chosen number will be a Fibonacci number

Suppose that I randomly choose an integer $x$ with $1 \leq x \leq n$ where $n$ is a natural number. What is the probability that $x$ will be a Fibonacci number?
0
votes
1answer
45 views

Random Walks proof SOS

Given this equation: $f_{2k}2^{2k}u_{2n-2k}2^{2n-2k}$=$f_{2k}u_{2n-2k}2^{2n}$ then it asks to "sum over k" to obtain this equation: $u_{2n}2^{2n}$=$f_0u_{2n}2^{2n}+f_2u_{2n-2} ...
0
votes
0answers
24 views

Reciprocal antiderivative of a process in an expected value

Given a stochastic process $X=\left \{ X_{t}:t\in [0,T] \right \}$, with known probability and spectral density function, is there a way to calculate or estimate the following expectation: $$\left ...
1
vote
0answers
52 views

Probability of random functions where domain equals co-domain

Given random function defined by $f: [n] \rightarrow [n]$, chosen uniformly, what is probability that the function is injective, surjective, or bijective? If $[n]$ is a set of discrete elements, ...
2
votes
1answer
97 views

Probability of picked cards to be smaller than the largest picked card

I have an assignment for my algorithms module that requires us, amongst other things, to find the equations for the following question. Edit - Question Updated You have n cards with pairwise ...
0
votes
1answer
65 views

Probability randomly picked card is smaller than another picked card

Given a set of m cards that have values pairwise different with range 1 to m, what is the probability that after shuffling the card, and picking two of them, the first one is larger than the second ...
0
votes
0answers
51 views

Computing an estimator for a piecewise distribution?

Suppose I have a random variable $X$ that follows a distribution with a piecewise function $f(x|\theta)$. What is the correct way to compute an estimator $\theta$ for this function? Should the ...
3
votes
1answer
40 views

Find probability of a Poission process.

Given that $N=\{N(t)\mid t\geq 0\}$ is a Poisson process with parameter $\lambda>0$ I need to find $P(N(3)=2\mid N(1)=0, N(5)=4)$ So this is a conditional probability (can anyone clarify if this ...
1
vote
0answers
96 views

Randomized packing of items

An adversary gives you a set of items whose total size is $x$ (he gets to choose how $x$ is distributed. e.g. there may be $k-1$ items of size $\frac{x}{k}$ and 2 items of size $\frac{x}{2k}$). The ...
0
votes
1answer
113 views

Frequency analysis/discrete uniform distribution in multiple choice tests

I may be using the wrong terms in the title but I read that if something is random then each character will occur an equal amounts of times. I read this when reading about the One-Time Pad cipher, ...
1
vote
0answers
25 views

Determinate State of Linear Congruential Generator from Results

I am curious on how someone would go about determining the state of a Linear Congruential Generator given its output. X(n-1) = (aX(n) + c) mod p Since the values ...
5
votes
0answers
204 views

expectation value for minimum distance between random variables

note: edited to clarify boundary issue Suppose $x_i$, $i=1\dots n$, are randomly drawn from a uniform circular distribution between 0 and 1 (using periodic boundaries). Let $d_i$ be the distance ...
0
votes
2answers
129 views

Addition of probabilities and gambler's fallacy

Say you have a 1 in 6 chance of winning a card game. The more times you play, the higher the odds of you winning. $$P(\text{win over 1 trial}) = 1/6 \\ P(\text{win over 2 trials}) = 1/6 + 1/6 \\ ... ...
2
votes
1answer
66 views

Probability that number begins with one

I have three very similar algorithms generating very different results. In all of them I'm calculating distribution of first number of random number. First algorithm Here I'm generating random ...
0
votes
1answer
35 views

Generation of “random” multilinear polynomials for testing non-negativity algorithm

Multilinear polynomial is a multivariate polynomial where the exponent is zero or one. My instructor suggests to test my non-negativity algorithm with ...
1
vote
1answer
92 views

Plotting psuedorandom jagged parallel lines

I'm very interested in the morphogenic freehand drawings of John Franzen. I am looking to develop an algorithm which can draw lines such as these with some "entropy". That is, somewhat jagged or ...
1
vote
2answers
54 views

How to proof the randomness of a number sequence?

I've got a sequence of numbers generator by a "random number generator". Is there a way or a method to proof the randomness of the generator? How would I even compare randomness of generators? Or ...
0
votes
2answers
49 views

What is the statistical difference (if any) between these two methods of generating an n-digit random number?

To preface, this question is coming from a software developer so it's written from that perspective. If I need to generate a random number with $n$ digits, I could do it in one of two ways. a. Ask a ...
1
vote
0answers
19 views

Good notation for many random points approximating an area.

I'm trying to say that as the number of random coordinate points points you plot approaches infinity, it is equivalent to an area integral where each point is an infinitesimally small $\mathrm{d}x ...
0
votes
2answers
59 views

Exercise from probability

In normal deck of cards each of the cards have some rank (2 have rank 2, 3 have rank 3, ... , J have rank 11, Q have rank 12, K have rank 13 and A have rank 14). 3 cards are drawn. We have the random ...