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Questions tagged [random]

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

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Definition of the rank of $x_t$ among $(x_1,…,x_T)$

I recently came across the following statement, but I don't understand how to implement it: Let ${x_1,...,x_T}$ be $T$ i.i.d observations of first differences of a variable $x_t$, and let $r(x)$ ...
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2answers
39 views

If $X_n$ and $Y_n$ are independent does $(X_n,Y_n)\overset{d}{\rightarrow}(X,Y)$?

More formally: If $X_n\overset{d}{\rightarrow}X$ and $Y_n\overset{d}{\rightarrow}Y$ and also $X_i$ and $Y_j$ are independent for all i,j; does $(X_n,Y_n)\overset{d}{\rightarrow}(X,Y)$? I am aware of ...
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21 views

Can a random number be created from competing non random numbers

Think about the following situation: Elections are held by dropping notes with the symbol of the political party to a ballot box. In order to save on time, a new automatic counting machine is ...
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45 views

Is this Forex trading algorithm flawed?

I'll try to explain this the best I can, I'm sorry for my lack of economic concepts and terminology. There's a Foreign Exchange Market where a trader gets to make predictions about the currency ...
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23 views

Escape time probability distribution

I have a system where a random walker is moving on $\mathbb{Z}$. However, at each point in $\mathbb{Z}$, there is a probability $q$ that an escape route exists along which the walker can escape. I ...
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20 views

Estimating sum of distinct numbers in a list

Suppose that each item on a list of $n$ items has a value attached to it, and let $ν(i)$ denote the value attached to the $i$ th item on the list. Suppose that $n$ is very large, and also that each ...
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34 views

Would sampling the decimal digits of $\pi$ generate a white noise signal?

Discrete r.v. $X = \pi(d)$ (defined in another q of mine). Discrete r.v. $Y = X - 4.5$. q1: Would it be incorrect to deduce $Y\sim U(-4.5,4.5)$ from $X\sim U(0,9)$? q2: If you answered no to q1, ...
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2answers
54 views

How do I evaluate (prove to myself) that a method for picking uniformly distributed values is correct?

To make this more specific, I show a broken procedure for generating random points in a circle and a correct (hopefully) procedure for generating random dates within an interval. I'd like to be able ...
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2answers
64 views

How to generate wrong numerical answers for a multiple choice test without giving information about the correct answer?

I want to generate $n-1$ wrong answers $a_2,\ldots,a_n$ for a multiple choice test given a correct number $a$. The problem is that I don't want the user to be able to guess the correct option with an ...
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1answer
34 views

Copula used for pseudo-random generation from continuous variables only?

I know multivariate pseudorandom generation from continuous distributions can be done using copulas and inverse transform sampling. The question is if copula have application in "discrete" pseudo-...
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1answer
23 views

Modeling phenomena using random variables

you could help me solve this exercise I have looked in books for help but I still can not solve it. Thank you. A load balancer in a cloud computing system is composed of N servers. The balancer, When ...
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45 views

Statistics - Stratified random Sampling

First, have a look at "Max Ft"'s answer to the following question: Stratified Sampling for Variance Reduction--Need Intuition as to Why it Works His answer makes sense for how stratified random ...
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0answers
17 views

Why quasi-random sequences are generated in the interval [0,1]? Is it a normalized sequence generation?

The quasi-random sequences are generated using low discrepancy sequences and Koksma-Hlawka inequality explains the quasi sequence clearly. However, it is observed that these sequences are generated in ...
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3answers
34 views

Arithmetic mean of error of N coin flips from N/2

When flipping $N$ fair coins, there is obviously an expected output of $\frac{N}{2}$ heads, but there will be some error from that value for individual runs. What I want is the arithmetic mean of ...
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2answers
37 views

getting 2 random numbers to add up to less than number n

So i'm trying to code a game for context. I'd like to be able to get 2 random numbers(a, b) that will add up to less then number ...
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1answer
22 views

Proof Random Sampling Interview

Got this algorithm in an interview. To prove that the algorithm randomly shuffles the array. The random sampling algorithm works as follows: ...
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26 views

N dimension random distribution with constraints

I am trying to draw $M$ random/semi-random numbers in $N$ dimensions applying some constraints. For instants I have a method that "selects" only the right points, but I am sure that it can be done ...
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1answer
67 views

an interesting game

Alice, Bob and Cindy are playing a game of a circle. Firstly, Alice starts by drawing a point around the circle. Subsequently, being aware of Alice's decision Bob makes his move. Finally, Cindy puts a ...
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1answer
22 views

σ-algebra and measure of the union of 2 sets. Based on measure theory.

A measure space $(\mathbb S,\mathcal S,μ )$ is not complete. The system of all its null sets is $\mathcal O$. Let $$\mathcal S' = \{A ∪ O : A ∈ \mathcal S, O ∈ \mathcal O\}.$$ The formula of the ...
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0answers
17 views

Generating random number with constraint [closed]

I am trying to generate N random or pseudo-random numbers in M dimensions, and trying to have a constraint between some of the dimensions. I have found an example in 2D where: alpha and beta are ...
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1answer
13 views

How do I choose a set of numbers from a PMF with a specified total?

So basically I'm choosing a set of numbers from a probability mass function, (say binomial or scale-free). By which I mean I'm performing a weighted choose operation using the PMF as weights. However ...
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2answers
51 views

A Hard Combination Probability Equation From A Reality T.V. Show

I was watching the T.V. show Survivor tonight and miserably failed at wrapping my mathematically out-of-practice post-college brain around a probability equation. Background: At the start of the ...
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39 views

Notation for random point on an area

Given that $S $ is a surface area. What is a good notation to indicate that a variable (position) $x_0$ is set to a random point on $S$. For now my solution is to simply write $x_0 \gets rnd(S)$, ...
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1answer
32 views

Find random non-almost-degenerated multivariate polynomials.

If I randomly draw parameters for a polynomial of degree $n$, say $P_n$, there seems to be big chances that this polynomial can be closely approximated by a polynomial of smaller degree $P_{n-k}, k\in\...
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1answer
21 views

what is the probability that the ID for the first registered user will start with the letter c and end with letter g

User IDs on an old computer system consist of 4 letter sequences from the first 8 letters of the English alphabet: a, b, c, d, e, f, g, h. Note that the same letter can be used any number of times in ...
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1answer
25 views

Calculating probabilities given CDF

Let $X$ be a random variable with CDF: $$ F_{X}(x) = \left\{ \begin{array}{ll} 0, & \textrm{$x<-1$}\\ \frac{1}{2}, & \textrm{$-1\leq x<3$}\\ 1-e^{-x}, & \textrm{$ 3\leq x $} \end{...
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0answers
15 views

The distribution of phase angle between identical zero mean Gaussian random signals?

I am trying to solve the 2013 paper set by ISRO for electrical engineers. I was hoping to get some clues on how to approach this problem - No 22. random signals which have gaussian distributions will ...
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0answers
26 views

Calculation of expected value in terms ACF

How to find expexted value of system output in terms of transfer function with knowing expected value of input and autocorrelation function of input? I should find Expectation of $y(t)=\int x(t-\tau)...
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0answers
37 views

How to calculate realization of a random process?

I am newly learner of subject of stochastic processes and my mind is full of questions. Hopefully I can ask one of them in a correct way. Suppose that X is an random variable which follows ...
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0answers
32 views

What is the conditional density function of $Z|Z = X$, where $Z = max\{X, Y\}$, X~exp($\lambda_1$), Y~exp($\lambda_2$) and X, Y are independent?

Given that $X $~$ $exp$(\lambda_1)$, $Y $~$ $exp$(\lambda_2)$, and $X$,$Y$ are independt. $Z$=$max\{X,Y\}$ Find the conditional density function of $Z$ given $Z$=$X$. I get pdf of $Z$ is $\...
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1answer
25 views

Demonstrate the mean of the sample variance

Let's suposse I have a vector of elements $x(n) = \{x(1), x(2), \cdots ,x(N-1)\}$ from a random process X of mean $\mu_x$ and variance $\sigma_x^2$. I want to see if I can stimate the mean and ...
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1answer
48 views

Hamming distance introduced by random permutation

Let $M$ be a random permutation matrix of size $N \times N$, i.e. a uniform random choice out of the set of all permutation matrices of size $N \times N$. Furthermore, let $v = (v_1, v_2, \dots, v_N)^{...
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1answer
18 views

Weighted random sample over continuous data

I'm attempting to write an algorithm which gives a random value x in the domain [0-1) and is weighted according to a function. I don't seem to be able to determine how to do this with continuous data, ...
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1answer
21 views

Generating random permutation with N cycle

Suppose we have integer list from 1 to N. I am interested in generating random permutations such that its cycle notation has only one N cycle. What algorithms are known to generate random N-cycle ...
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19 views

Iterative Homing Function

For a personal project of mine, I need a mathematical function which generates values. In Computer Science terms, this is a PRNG, however I can't find one applicable to my problem. $h(x_0, params) = ...
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0answers
24 views

Probability of n points from a square area being all on their convex hull

If we uniformly randomly generate n points in the unit square, what is the probability of all of them laying on their convex hull, i.e., they form a convex n-gon? I've been searching the internet and ...
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Distribution of overlapped sampling

Given $n$ i.i.d. random variables $X_i$ for $1 \le i \le n$. Consider a moving block bootstrap sampling with block size $l$: $B_i = (X_i, \ldots, X_{i + l - 1})$ for $1 \le i \le n - l + 1$, there are ...
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1answer
44 views

Can anyone help me on any of these parts? [closed]

I'm an undergrad student taking a grad level probability class. I am not sure how to do any of these problems so if anyone can help me with any of the parts i would really appreciate it. The set B is ...
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Expected number of neighbors in an Area with Random Uniform distribution

In an area of ${100m^2}$ 19 sensor nodes are uniformly and randomly distributed. Root node is located at the center of this area. Each node has a transmission range of 40 meters in all directions. All ...
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17 views

Is an exponential function of a stochastic process a smooth function?

Let's say I have an Ito process $X_t$, and another process $Y_t=e^{\int_t^{t+\delta} X_s ds}$. I want to know that quadratic variation of $Y_t$ and another process. I know that the quadratic ...
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1answer
33 views

First Occurrence of a Type of Card in a Randomly Shuffled Deck

Suppose that I have a deck of $T$ cards, with some set of size $X$ of them having some property. If it helps you to think of a specific property, in a poker deck they could be all the hearts, in a ...
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1answer
18 views

Would this method approximate a uniformly distributed random points on sphere?

I know there are several ways to generate uniformly distributed random points on the 2-sphere $S^2$. But I would like to know if my method does the same job, although it is very inefficient. Say, I ...
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1answer
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Proof of the statement based on measure theory. [closed]

Let $A, A' ⊂ 2 ^S$. Prove that: If $A ⊂ A'$ , then $σ(A) ⊂ σ(A')$.
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1answer
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Joint probability distribution function and expected value

Lets say for we have a first dice and a second dice, with X representing the face of the first dice and Y representing the face of the second dice. I know that E(X) = E(Y) = 3.5 $$ E(XY) = \sum_{(x,y)...
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1answer
46 views

Billiards in a holey square

Suppose you start a point-billiard (or light ray) in a square at a random location, shooting off at a random angle, reflecting with angle-of-incidence equals angle-of-reflection. In general, because ...
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30 views

simulation/ probabilty

Suppose a population control plan for the country of Transylvania allows parents to have at most four children each, and they must stop having children when they get two girls. Explain how to ...
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0answers
18 views

Number of distinct sites visited by a random walk in one dimension

Is there a paper which explains how the number of sites visited by random walkers on a one dimensional lattice evolves depending of the number of steps ? I'm looking for a way to demonstrate that for ...
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0answers
18 views

(Non-replacement deck draw)Adding together increasing probability of drawing target card?

This is more a question to explain if there is any value in simply adding the probability of each subsequent draw from a deck to get a target card? What I mean is: 1/52 + 1/51 + 1/50 + 1/49 .... ...
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23 views

Taking SRS of a non normal/normal distribution

I was studying how taking Simple Random Samples of a non-normal distribution change the shape of the distribution. But how do I exactly take an SRS of a distribution? For example, consider a normal ...
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Covariance matrix under multiplication with independent random variable.

assume two dependent random variables X and Y with their covariance matrix $\Sigma_{ij}$. Now assume one multiplies X with another independent random variable Z. The variance of the resulting random ...