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Questions tagged [random]

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

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Randomized Submatrix of a Sparse Matrix

I have a sparse square matrix $A$ with size $n \times n$ and number of nonzero entries $nnz$. The goal is making a sub-matrix $B$ with $s$ nonzeros which are randomly chosen from $A$. Duplicates are ...
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28 views

Let X be distribution over N (the set of non-negative numbers), with mass P(X=i) = a/2^i, what is the value of a?

I am struggling with solution for following problem part of course about probabilities random variables, seek your kind help to show how to solve it, Let $X$ be distribution over $N$ (the set of non-...
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Sample from random normal with sliding mean

I have a uniform random variable $x$ and a normal random variable $z = \mathcal{N}(x, \sigma)$ (i.e. the mean is given by $x$). How can I draw samples $(X, Z)$ such that they correspond to their ...
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21 views

The independence of two random uniform distribution random variables

$y_1 = x_1 + x_0$; $y_2 = x_2 + x_0$. Suppose that $x_1$, $x_2$, and $x_0$ are independent with each other. They all follow the uniform distribution in $[0, 1]$. Then, I want to know if $y_1$ and $...
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Random walks in different directions?

Assume a person random walker takes equal steps to the right or left with equal probability. Probability that taking n steps, the person walking will be displaced 1 standard deviation or greater in ...
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58 views

How many roots exist for $y=sec(x)$

In the interval $( - \pi ,\ \pi ]$.There are 2 roots exist mentioned in the book. Could anyone please explain how? Exact question from book : Let $Y=\sec X$ .Compute $f_Y(y)$ in terms of $f_X(x)$ ....
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22 views

Simulate a discrete random variable

We have a discrete random variable $X$ with the following probability distribution \begin{equation*} p(X=i)=p_i,\quad i=1,2,\ldots 1000, \quad \sum_{i=1}^{1000}p_i=1. \end{equation*} How we can apply ...
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Probability of having a link in union of Erdos Renyi random graph

We have two Erdos-Renyi random graphs, $G_1$ and $G_2$, generated with probability $p_1$ and $p_2$, respectively. If we take the union $G_1$ $\bigcup$ $G_2$, we obtain another Erdos-Renyi graph, $G_3$...
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31 views

Let Z ∼ Exponential(4). Compute each of the following. (c) P(Z^2 ≥ 9) (d) P(Z^4 − 17 ≥ 9) [closed]

I got part C by changing it to 1- P(-3 < Z <3), but it doesn't work for D.
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18 views

probability after ten draws

I would like to know if my partial solution is appropriate: We have ten urns, in each urn we have 2 balls: in 1st urn - 2 balls of number 1 in 2nd urn - 2 balls of number 2 . . in 10th urn - 2 ...
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Question on Random Variables from the textbook “Mathematical Statistics and Data Analysis” by John Rice

If $U$ is a uniform random variable on $[0,1]$, what is the distribution of the random variable $X=[nU]$, where $[t]$ denotes the greatest integer less than or equal to $t$? I've tried searching ...
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Connections between the randomness of the normal distribution and Textrank?

In a TED speech on 8:40 the mathematician said that: This algorithm uses the laws of mathematical randomness to determine automatically the most relevant web pages, in the same way as we used ...
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1answer
33 views

Probability two sequences of coin flips reach consecutive heads at the same time.

Two people start flipping coins. The probability of heads is 0.5 (bonus if you can do it for $p_1$ and $p_2$). What is the probability that both will hit two consecutive heads simultaneously (as ...
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60 views

Sum of Uniform(5,10) random variables to get more than 30

Let $X_i$ be i.i.d. $Uniform(5,10)$, and let $Y_t = \sum_{i=1}^t X_i$. Let $T = \mbox{inf}\{t:Y_t \geq 30\}$, what is $\mathbb{E}[T]$? At first I thought this was similar to Choose a random number ...
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40 views

Reachability of points on Manifolds

I was thinking with a friend that on a surface some points are more reachable than other.In the sense that their average distance to the other points is lower. e.g. suppose that we have a circle in a ...
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Expectation of function of random sinusoidal process

I have a random sinusoidal process as follows. $x(t)=Xsin(2πft+θ)$ Here, $θ$ is a noise in the phase that uniformly distributed in range $(-π,π)$. $\ $ I need to estimate the value of $E[x(t)x'(t)]...
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Performance of conventional estimation approaches for sparse recovery

If we use conventional estimation methods (like Least squares or MMSE) to recover a sparse vector for which we have random measurements, is the result accurate? Why?
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44 views

Does Ramsey theory prove that all sufficiently long random sequences can be slightly compressed?

First, my apologies if this has already been asked and answered. I did search this community for five to ten minutes looking for similar questions and found none. My lay understanding of Ramsey ...
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1answer
30 views

Random number generation: divisibility

I'm interested in generating random numbers. I have a distribution [for simplicity let it be uniform distribution] of some event occurrence, i.e. the event (visits to a doctor) occurs between $1$ to ...
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1answer
35 views

Random number generation: changing time interval

I'm interested in generating random numbers. I have a distribution [for simplicity let it be uniform distribution] of some event occurrence, i.e. the event occurs between $1$ to $3$ times per year. ...
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1answer
23 views

Polynomial with random roots

Hypothesis: all polynomials and operations are defined over a finite field, $\mathbb{F}_p$, where $p$ is a prime number. In the literature, especially in cryptography, a random polynomial defined as ...
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17 views

If I generate a number from 1 to 100, there is an equal chance to hit any number, but how do I get an exact % chance

I am creating a game, and I feel like I am going about the random generation of a number wrong. I have a set plan that the user has a 5% chance to win prize A, and a 10% chance to win prize B. 40% to ...
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Clustering of pseudo-random sequences based on transition matrices

THE BACKGROUND A lot of malware is propagated through the internet via so-called DGAs, i.e., algorithmically-generated domain names that serve as rallying points between the infected clients and the ...
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Exercise that requires some ability to work with sets, cartesian product of sets, and random variables

I have to solve a tricky exercise that requires some ability to work with sets and random variables. I would like your help with this because I'm unable to see how to proceed. Construction of $\...
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How to create an injective function to generate pseudo-random numbers with seed

Let's call A the set of all the n-digit natural numbers (base 10). So with n=3, they would be 000, 001, 002, ... 999 Basic question: I need to create a mathematic function with this features: it ...
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1answer
35 views

Alternative ways of sampling from a distribution

I have recently been working on some numerical algorithm that required me to pick a random element $r_i$ from a finite set $R$ with probability $p_i$. This is a fairly standard procedure and many ...
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29 views

reference request - Practice problems for probability theory.

I need some good probability theory practice problems on the following topics - Binary strings ( Bit strings ) generating random permutations using bit strings Coin toss problems where each toss is ...
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19 views

Optimal Stopping Problem w/ “Going Backwards”?

I'm currently reading Algorithms to Live by and one application of the mathematical optimal stopping problem was mentioned as a framework for solving problems with ...
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16 views

What is the product of two Gaussian random matrices?

Suppose you have two i.i.d $K \times N$ random matrices $A$ and $B$. Both matrices have complex valued entries taken from a Gaussian distribution with $\mu = 0$ and normalised variance $\sigma^2 = \...
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Can a stochastic process has time dependent mean and time independent autocorrelation?what is the autocorrelation of the process through a LTI system?

I have this process: $$X(t)=A\cos(2\pi f_0t+\Phi)\ast \operatorname{rect}\left[\frac{t-T/4}{T/2}\right]$$ where: $A$ and $\Phi$ are uniform random variable in $[0,\pi]$ statistically independent $\...
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Mean and correlation of product of two random processes

I have two random process: $$A(at)$$ $$cos(2\pi f_0t+\Phi)$$ with these hypothesis: $a$ and $f_0$ are constant $\Phi$ is uniformly distributed in $[0,\pi)$ $A(at)$ is WSS I must calculate the ...
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32 views

Random point within triangle + within 2 radiuses

I am working on pathfinding for a 2D game, and need to obtain a random point within a triangle. This is simple, I am just sampling 3 times from a uniformly distributed random variable, then blend the ...
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1answer
38 views

What are examples of pseudorandom functions that can be preformed without the assistance of a computer?

I'm trying to generate a seemingly random list of integers without the use of a computational device; one capable of being unraveled with a mathematical function. What's the best way to devise a ...
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using monte carlo to determine uncertainty.

In my thesis there are some uncertainties (for example in geometry: the diameter of cylinder, the height ,.. or the temperature of inlet fluid ) and I want to know what is the effect of them in my ...
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Regularity of zeros in a sparse matrix

I have a large matrix which is around 70% zeros. How can I test whether there is some statistical regularity to those zeros, as opposed to being randomly distributed?
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How to calculate a pseudo random Catalan number? [closed]

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the ...
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53 views

Write some probabilities using a common cumulative distribution function

Consider the random variables $Y,\epsilon_1, \epsilon_2$. $\epsilon\equiv (\epsilon_1, \epsilon_2)$ has cumulative distribution function (cdf) $F$. Let $u_1, u_2$ be some known real-valued parameters....
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63 views

why monte carlo method use random sampling? and not a specific numbers? [duplicate]

in calculating the area of a circle in a square we use random points to calculate the fraction of circle! but why we dont assume a simple grid and put our points in the center of it. this seems more ...
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25 views

Express $\mathbb{P}(\underline{y}_k\leq Y_k\leq \bar{y}_k \text{ }\forall k) $ in terms of cdf

Consider the k-variate random vector $Y\equiv (Y_1, Y_2, ..., Y_K)$ with cumulative distribution function (cdf) $F$. How can I express in terms of $F$ the following probability: $$ \mathbb{P}(a_k\...
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Probability simple random walk does not return $M$ times

Consider a simple symmetric random walk on $\mathbb{Z}$ starting from $n_0 >0$. It is well known that the probability that the simple random walk does not visit the origin in the first $k$ steps ...
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Split interval into random regions

I'm having troubles comming up with algorithm, that would split interval of integers (lets say from 0 to 1000000) with these parameters : There are N kinds of regions. Neighboring regions cannot have ...
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1answer
81 views

Is it possible to generate random numbers out of nonrandom numbers? [closed]

Let's say we have thousands of pseudo random sets which has been generated by different pseudo random generators, is it possible to have a true random product of these sets? What if we take thousands ...
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43 views

What does it means for a sample to be random?

For a sample to be random, I thought it means that every member has an equal chance of being selected. However, it seems like it is insufficient to just say the above. May I know what is the proper ...
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42 views

Mean Distance From Nearest Neighbor

Let $x_i^{(n)}$ (with $i=1,\ldots,d$ and $n=1,\ldots,N$) be $d\times N$ i.i.d variables, normally distributed with zero mean and unit variance. What is the mean euclidean distance between the vector $(...
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How is the Standard Deviation affected when more (bounded) random numbers are included in a sample?

If I generate random numbers between two bounds, e.g. $0$ to $100$, will the standard deviation converge to a particular value the more random numbers I generate?
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Does generating more random numbers decrease the standard deviation? (In this particular allocation problem)

Say we want to bake 6 cookies with at least 3 chocolate chips each. We will randomly allocated chocolate chips to each of the 6 cookies until each has at least 3 chocolate chips. The minimum solution ...
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46 views

Max value of random numbers [closed]

I have a dice with 100 sides. If I roll the dice n times, what will the maximum value of the n numbers statistically be? Please keep it as simple as possible, as I want to turn the answer into an ...
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27 views

Super-ellipse Point Picking

This is a cross-post from Stack Overflow by a user recommendation. https://en.wikipedia.org/wiki/Superellipse I have read the SO questions on how to point-pick from a circle and an ellipse. How ...
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76 views

Can you make a reliable random-number generator from the stock market?

Can the stock market be used to make a reliable random number generator? I'm not necessarily asking if it follows a random walk which was discussed more here, nor am I asking if everything about it ...
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111 views

Can we find every finite sequence of $\pi$ within $\pi$?

Inspired by one of the top posts I was wondering if $\pi = 3.14159\dots$ were normal--as in you could find every finite string of numbers within $\pi$'s digits--would that mean we could find every ...