Random Definition and 1000 Threads

40 teams are taking place in a knock-out competition in which there is no seeding. They all have rankings determined by previous performance. The pairings are decided by a completely random draw, e.g. all the team names are put in a hat and drawn by a neutral party. What are the chances of the...

Consider a random walk (in any dimension) with N steps and a step size of 1. Take a real number \alpha > 0 and consider another random walk which takes \alpha^2 N steps but wil step size \frac{1}{\alpha}. I immediately noticed that the mean deviation after the full walk in both cases is the...

Hello everyone, I am trying to understand markov random fields and how it is related to the Gibbs measure and basically trying to understand the Gibbs-MRF equivalancy. Anyway, while browsing Wikipedia documents, I was looking at the page on MRFs and when I came across the following line...

Hello Let's say we have some continuous i.i.d random variables X_1, \ldots X_n from a known distribution with some parameter \theta We then place them in ascending order X_{(1)}, \ldots X_{(n)} such that X_{(i)}, < X_{(i+1)}. We call this operation T(\mathbf{X}) where \mathbf{X} is our...

Quick random questions to help me clear stuff up :) Hey I'm studying for my final exams and oh my have I forgotten a lot of things. so I have a few questions, answer them If you wish and/or can: If f \propto a and a \propto 1/m why can we say that a \propto f/m ?? secondly, I have...

A problem in this book asks for the most probable value of a random variable x. As far as I know, if a random variable has "most probable value" then it isn't a random variable. The problem is attached. It is the second question in part b. Could the answer be that there is no most probable...

Hi all, in text the formula for scaled random walk is: W^(n) (t) = (1/√n) M_nt in the example it says that: set t=0.25, n=100 and consider the set of possible values of W^(100) (0.25) = 1/10 M_25. This random variable is generated by 25 coin tosses, and since the unscaled random walk...

Basically i got to solve two problems that can be described as: if you throw 80 apples at 100 buckets randomly, and each apple must enter a bucket. How many buckets will on avarage contain 0 apple's? how many wil contain 1?, and 2?, and more? problem two: if a given number of random...

i have this question i do find the distribution like this figure : and i plot the y like this: now i want to find the distribution of y i tried to take the distribution for each interval in Fx(x) like this : but the solution in the book said : who is wrong me or the book...

I have a problem calculating the following probability. There are two signals A and B each consisting of a series of "pulses" at times {tA0, tA0+Δt, tA1, tA1+Δt, tA2,tA2+Δt, ...} and {tB0, tB0+Δt, tB1, tB1+Δt, tB2, tB2+Δt,...} The signal A is "on" in the time intervals [tAn...

Homework Statement A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with any opponent is independent of previous encounters. The player continues to contest opponents until defeated. What is the probability...

Hi all, I am really confused about the random variables Toss a coin three times, so the set of possible outcomes is Ω={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Define the random variables X = Total number of heads, Y = Total number of tails In symbol, X(HHH)=3...

Hi there, I am currently reading Rohatgi's book "An introduction to probabilty and statistics" (http://books.google.de/books?id=IMbVyKoZRh8C&lpg=PP1&hl=de&pg=PA62#v=onepage&q&f=true). My questions concerns the "technique" of finding the PDF of a transformed random varibale Y by a function...

Hey guys, I have a quick question. Suppose X is a chi squared random variable with n degrees of freedom and Y is another independent chi squared random variable with n degrees of freedom. Is X/Y ~ 1 ? Intuitively, it makes sense to me but I'm not too sure.

Homework Statement I must calculate the characteristic function as well as the first moments and cumulants of the continuous random variable f_X (x)=\frac{1}{\pi } \frac{c}{x^2+c^2} which is basically a kind of Lorentzian.Homework Equations The characteristic function is simply a Fourier...

Hi, my name is Ofek and its my first post here. hope to be clear and if not I'll try to be more specific next time. Link for the article: http://arxiv.org/pdf/cond-mat/9708043.pdf Writen by N. S. Branco The model H = J*ƩSiSj + ƩΔi(Si)^2 - first sum over nearest neighbors and second sum...

This is a question relating to lotteries. Bascially everyone says that each draw is totally independant of each other. So the probability of generating a sequence of numbers each time is the same no matter what the numbers are. However for two draws, there must be a way to calculate the...

Hi, I'm trying to write a short code in Mathematica that can generate random real numbers in - say 5 secs, and then plot this against any specified range I want. An additional complexity is that the function I'm generating the random numbers for is embedded in an integral. Here's an example...

I am interested in the following random walk scenario, where a walker starts at a defined position greater than 0, say A, and then makes a "decision" to walk to either walk "b steps to the right" or walk "c steps to the left." He will choose the first option with probability p, and the second...

Homework Statement Take Ω = [0, 1] and P the uniform probability. (a) Give an example of two random variables X and Y defined on Ω that both have the same Bernoulli distribution with parameter θ = 1/3. (b) Give an example of such random variables that are independent, and not independent...

Homework Statement Give the value of u_0.Homework Equations Let p>q>0 with p+q = 1 and a = q/p < 1. Let X_n denote the random walk with transitions X_{n+1} = CASE 1: X_n + 1 with probability p and CASE 2: X_n - 1 with probability q. For i ≥ 0, we set u_i = P(X_n = 0 for some n ≥ 0|X_0 = i)...

Homework Statement The graph of y=f(x) is shown below. http://Newton.science.sfu.ca/cgi-bin/plot.png?file=public_public_1346904771_18810161_plot.data Rank the following from smallest(1) to largest(4). f−1(0) f(0) f(5) f−1(5) Homework Equations none available The...

Some things are physically impossible, but mathematically possible (like exactly bisecting a line segment). Some things are both physically and mathematically impossible (like exactly trisecting an angle "with a ruler and compass".) Things mathematically impossible are proven to be so...

I read about the random walk the other day. The simplest 2D form, where you start at zero and move up or down one unit at random, both are as likely. To get an the average distance from zero after N steps, the following argument was used: The distance after one step is 1. If after some steps...

Homework Statement Let f(x)=x/8 be the density of X on [0,4], zero elsewhere. a) Show that f(x) is a valid density and compute E(X) b) Define Y=1/X. Calculate E(Y) c) Determine the density function for Y The Attempt at a Solution a) is just really basic. I've solved that one. b)...

I have an exercise that I do not understand how to solve (statistics and probability is really my weaker part...). The exercise goes as follow: In a certain population, the random variable Y has variance equal to 490. Two independent random samples, each of size 20, are drawn. The first...

I've been thinking about what random actually is and let me give you an example. If you made a machine that flips a penny, put the machine and and penny in a small room, place the penny upon the flipper and let it flip, now so long as the penny was placed in the exact same position every single...

Hi there, (to mod: not sure where to post this, please move if I've got it wrong) I have a grid of values with 41x161 nodes describing some parameter space. Each node has an associated value, λ, which represents the uncertainty of the parameter choice at that node. I want to make/find an...

Homework Statement The probability of being dealt a full house is approximately 0.0014. Find the probability that in 1000 hands of poker you will be dealt at least 2 full houses Homework Equations I can use binomial distribution. The Attempt at a Solution The probability of getting...

Hello everyone! I'm coming to notice day by day how our education is purely focused on memorizing and applying formulas rather than understanding the concept. Assume we have the following: $X = aR + N$, and $Y = bG + W$, where $X, Y$ are random vectors, $R, G$ are strongly correlated random...

Hi everybody, I try to figure out connections and differences between random variables (RV), random processes (RP), and sample spaces and have confusions on some ideas you may want to help me. All sources I searched says that RP assigns each element of a sample space to a time function. I want...

for an observer arriving at a random time t_1, where t=0 is the time when the last car passed, i got the following pdf for Δ^∗- the time the observe waits until the next car: ρ_{Δ^∗}=\frac{1}{Δ^∗}⋅(e^{-\frac{Δ^∗}{τ}}−e^{-\frac{2Δ^∗}{τ}}). the mean is τ, like the book said and it goes to 0 for...

It seems to me that the recent deeds of ……… ………. cast a serious aspersion on the reputation of higher learning and the worth of knowledge in general. That is a depressing if not completely unacceptable predicament in many ways. I don’t know where he was studying, with whom, in what topic area...

Dear all, I apologize if it is the wrong place, I don't know where I had to post this question since I'm not a mathematician. Well, suppose you have a set of numbers which can be describe by a unknown distribution. I just like to know whether we can use those numbers to generate a set...

Is the use of the term random a valid scientific explanation or just a pseudoname for unknown? I'm asking if it isn't essentially illogical to ascribe the existence of an event, (e.g the origin of the universe) to a random predecessor event. My humble understanding of logic adheres to a cause...

Homework Statement Hi, I would like to generate a random delay time and value in testbench. This is what I did: for(i=0;i<300;i=i+30) begin j = i + {$random} % (300 - i) // MIN + {$random} % (MAX - MIN ) #j b = {$random} %3; #3ns b = 3'b000; end I want to generate random...

I'm reading through Reif's "Statistical Mechanics" to prepare for the upcoming semester. Basically, a drunk guy takes N total steps, n1 to the right and n2 to the left. The probability that the current step will be to the right is "p," while the probability that the current step will be to the...

Homework Statement Suppose X is a discrete random variable whose probability generating function is G(z) = z^2 * exp(4z-4) Homework Equations No idea The Attempt at a Solution I'm thinking that due to the exponent on the z term, that the exp(4z-4) would be the P[X=3] =...

Hi everyone, I am trying to generate 200 random numbers from an exponential distribution which have to add to one. I guess I need a loop where in each step I generate a random number from the exponential distribution and check the sum, if it is less than one I add the number to a list and if...

Absolutely Stunning Plot of a "Random" Sequence (Picture Included)--Need Explanation So I created 10000 waves of varying heights, 50% of the waves were 2 feet, 30% 1 foot, 15% 3 feet, 4% 4 feet, and 1% 5 feet tall. I generated 10000 "random" numbers with the statement "=Rand()" (this generates...

EDIT: Oh and I forgot that $p_Y(y) = 0$ otherwise.

You are given a random exponential variable X: f(x) = λ exp(-λ x). Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X: Y = IP(X), Z = FP(X). Which is the following conditional probability: P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?

Hi, can someone who is familiar with the analysis of random walks (statistical mechanics, condensed matter physics etc.) help me on solving a particular problem? We define the following random walk, the random variable w(t) is evolved as w(t+1)=w(t), with probability of...

Hi, I have a random variable X with some zero-mean distribution. I have a function Y of this r.v. given by something complicated Y=(a+X)^\frac{2}{3} Is there an explicit way of finding the distribution of Y or even its mean? Thanks

Homework Statement I'm trying to show that U(X+Y) = X in distribution, where X and Y are independent exp(λ) distributed and U is uniformly distributed on (0,1) independent of X+Y.Homework Equations The Attempt at a Solution X+Y is gamma(2,λ) distributed. But I can't figure out how to deal with...

In random walk, what is the meaning of "first return visit" I am reading it at http://www-math.mit.edu/phase2/UJM/vol1/RMONTE-F.PDF

Homework Statement In an experiment to determine the Ar of Li, the % error due to random errors was calculated to be 12.1%. However, the literature value is 6.941 and my calculated value is 7.5 which means my % error s 7.45. Homework Equations Usually, the error due to the literature...

I have seen the following "extension" of discrete random variables definition, from: pediaview.com/openpedia/Probability_distributions (Abstract) "... Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf)...

About the definition of "discrete random variable" Hogg and Craig stated that a discrete random variable takes on at most a finite number of values in every finite interval (“Introduction to Mathematical Statistics”, McMillan 3rd Ed, 1970, page 22). This is in contrast with the assumption that...

Hello, I apologize in advance if I have missed the right place to ask. I'd be grateful if you could forward me to the right place, if that is the case. Google didn't help, so maybe someone here can point me in the right direction: 1) "If the input to a LTI system is a Gaussian random...