Random Definition and 1000 Threads

1. Imagine a positive point x not equal to zero. 2. Consider a randomly chosen point y with distance to zero less than x. 3. Let y=x. Repeat #2. 4. Is the sum of the y-values finite as y approaches zero?

Let X_1, X_2, ... be a sequence of random variables and define Y_i = X_i/E[X_i]. Does the sequence Y_1, Y_2, ... always convergence to a random variable with mean 1?

i am tying to analyze a random walk on an integer lattice \mathbb{Z}^k. for k=1, what is the probability that after steps the drunkard's distance from the origin is lower than \sqrt{n}?

This just came into my head. I don't think I really understand the significance of Maxwell's demon. Please don't try to explain it to me. It's just a random thought.

Hello there, I am wondering if somebody could help in an issue far from my expertise. I have some data which is reasonable to conjecture could be modeled with a random walk with drift. I am struggling though to understand how to estimate from the empriic data the most likely drift and...

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

Let be $X_1, X_2, ..., X_n, ... $ independent identically distributed random variables with mutual distribution $ \mathbb{P}\{X_i=0\}=1-\mathbb{P}\{X_i=1\}=p $. Let be $ Y:= \sum_{n=1}^{\infty}2^{-n}X_n$. a) Prove that if $p=\frac{1}{2}$ then Y is uniformly distributed on interval [0,1]. b) Show...

I am wondering if I can find a decomposition of Y that is absolutely continuous nto two i.i.d. random variables X' and X'' such that Y=X'-X'', where X' is also Lebesgue measure with an almost everywhere positive density w.r.t to the Lebesge mesure. My main intent is to come up with two i.i.d...

given the following Probability density function: f x,y(x,y) = { 0.5, ( 0<y<1, 2y-x<2, 2y+x<2 } 0, else and i need to find f z(z) while z=y-x i got really confused while trying to calculate the borders of x and y for the integration. i would be really thankful for someone explaining...

Given the fact that X and Y are independent Cauchy random variables, I want to show that Z = X+Y is also a Cauchy random variable. I am given that X and Y are independent and identically distributed (both Cauchy), with density function f(x) = 1/(∏(1+x2)) . I also use the fact the...

Hello, I don't really know if this is considered a challenging problem but this is not for homework: You're given a set of numbers S of size n. From S, you draw a random sample A, |A| < n. From S, you draw a random sample B, |B| < n. Sampling doesn't remove items from S. What is the...

Dear All, I am simulating a random walk on a sphere with unit radius. I want to move from current location p_t to the new location p_{t+1} along the big circle, whose arc has an angle omega relative to p_t's latitude. I tried using the law of cosine. But at the poles, the law of cosine...

One day I just put on my [SIZE="5"]polarized sunglasses, and on the road, I looked at cumulonimbus cloud probably in the congestus stage in a system with many other cumulus clouds (those big puffy clouds), and a single giant cumulus cloud appeared yellow-ish when wearing the polarized sunglass...

I have: $Z=X_1+\ldots+X_N$, where: $X_i\sim_{iid}\,\text{Exponential}(\lambda)$ $N\sim\,\text{Geometric}_1(p)$ For all $i,\,N$ and $X_i$ are independent. I need to find the probability distribution of $Z$: $G_N(t)=\frac{(1-p)t}{1-pt}$ $M_X(t)=\frac{\lambda}{\lambda-t}$...

Homework Statement Z=X_1+\ldots+X_N, where: X_i\sim_{iid}\,\text{Exponential}(\lambda) N\sim\,\text{Geometric}_1(p) For all i,\,N and X_i are independent. Find the probability distribution of Z Homework Equations G_N(t)=\frac{(1-p)t}{1-pt} M_X(t)=\frac{\lambda}{\lambda-t}...

Ok I've been surfing trough the internet for quite some time now trying to find a solution to my problem but nothing similair pops up. This is my problem: http://i40.tinypic.com/295dc9f.png For some peculiar reason the structure tends to bend over to the left. I have no idea why and I've...

I think I understand the concept of random variable (for example, the number of heads when three coins are tossed together or the temperature of a place at 6.00am every morning). I am, however, confused as I have seen some material which refers even the values taken by a random variable (or...

how is bayesian inference actually applied? Say I have (100samples) a series of random numbers between 1 to 10. How do I test for the hypothesis that "there is a bias for the numbers 5,7" ?

There are plenty example of functions are random variables from my class note. I only interested of thinking up functions are not random variables. If you know functions are not random variables please please reply this post. This class is about set theory, probability measure, Borel...

Homework Statement If R1 and R2 are two uniformly distributed random variables on the interval [0,1]. What is the density function Z=R1*R2? Homework Equations I'm not sure actually The Attempt at a Solution I have tried to manipulate with moment generating function (which i...

Homework Statement The n random variables X_{1}, X_{2},..., X_{n} are mutually independent and distributed with the probability density f(x)=\frac{1}{\pi(1+x^{2})} i) Find the probability density of the average Y=\frac{1}{n}\Sigma^{i=1}_{n}X_{i} ii) Explain why it does not converge...

Homework Statement If you were taking a random sample of size n (n=2m+1 odd) from Uni(0,1) How do you find the mean and variance of the sample median? Homework Equations In order to find the mean and variance of the sample median you need to start with the sample median itself. Using...

Hi All, By definition, the sum of iid non-central chi-square RVs is non-central chi-square. what is the sum of ono-identical non-central chi-square RV. I have a set of non zero mean complex Gaussian random variables H_i with a mean m_i and variance σ_i . i=1...N. H the result of their...

Hi all, I have a random variable (RV): X=\text{max}X_i+X_j where Xi and Xj are two different RVs from a set of i.i.d N RVs. I need to find the distribution of X. What is the most efficient way? Thanks in advance

Hello! I am trying to understand an example from my book that deals with two independent Poisson random variables X1 and X2 with parameters λ1 and λ2. The problem is to find the probability distribution of Y = X1 + X2. I am aware this can be done with the moment-generating function technique...

Hi all, I got stuck with the following problem: Let X, Y and Z be three random vectors of the same length drawn from a continuous random distribution. where Z is independent of X and Y but Y=f(X) with a non-linear function f. Can I claim that: 1. Z^{T}X\neq 0 almost surely...

Homework Statement Show that if X is a bounded random variable, then E(X) exists.Homework Equations The Attempt at a Solution I am having trouble of finding out where to begin this proof.This is what I got so far: Suppose X is bounded. Then there exists two numbers a and b such that P(X > b)...

Why are there 8 possible moves in 3D random walk? With R being the distance from the origin, how is its relationship with the number of steps and dimensionality? Thx!

Einstein strongly believed in determinism. Some physicists today like Michio Kaku are leaning toward indeterminism. I have many of my own reasons but I'm on Einstein's side. I want to discuss, not fight. Listen to what other posters have to say before refuting it.

Is there anything in the physical world that is actually random even after we were given every single bit of information needed to calculate an outcome? Rolling a die or flipping a coin doesn't count, because if we did all the calculations, we would be able to calculate what the outcome would...

Homework Statement A Normally distributed random variable with mean μ has a probability density function given by _ρ_...*...((-ρ2(x-μ)2)/2δ) √2∏δ|...e^ Homework Equations Its standard deviation is given by: A)ρ2/δ B)δ/ρ C)√δ|/ρ D)ρ/√δ| E)√δ|/2ρ The Attempt at a Solution...

Hi. I would like to find out the probability distributions function of the sum of 5 independant random variables. They are a sum of errors: 1%, 1%, 0.1%, 0.1%, 1%. I think this is the convolution of all these. So the limits are +/- 3.2% I know the convolution of 2 square pulses becomes a...

http://img844.imageshack.us/img844/8333/1111jx.png Homework Statement With which probability, starting in g, node d gets hit before node e?Homework Equations The Attempt at a Solution I think the probability of hitting each node starting in g is the following: p(g) = 1 p(c) = 1/2 p(a) =...

Homework Statement Suppose we have a function, f(x,y) = e^-x * e^-y , 0<=x< ∞, 0<=y<∞, where X and Y are exponential random variables with mean = 1. (For those who may not know, all this means is ∫(x*e^(-x) dx) from 0 to ∞ = 1, and the same for y) Suppose we want to transform f(x,y) into...

Hi. Why in all literature bus arrivals are referred as independent random variables (Poisson as well)? Is there any reference where there is some math explanation except intuitive approach which of course tell that there is no correlation between 2 bus arrivals? Best regards

Hi, I want to create a generator for random irreducible N times N matrices, where N is a given integer. For now I'm using this trick: Generate a N-length array H_i with purely random numbers Creating the matrix by assigning element A_{ij} = \min(1,\exp[\beta (H_i-H_j)]) This matrix is...

Hi all, I am currently doing my Final Year Project on the topic of Optimal Placement of Suicide Bomber Detectors. Given 2 dependent bomb detectors, I am trying to prove that the probability of detection in the intersected area will be larger than the individually covered areas, by working...

Suppose the random varaible Y has non-zero probability at 0,1,2,3,... (i.e. the support of Y is the set of non-negative integers). Define a random variable W: W=0 ,if Y=0,1,2,or 3 --=Y-3 ,if Y=4,5,... Define a random variable Z: Z=max{0,Y-3}=0 ,if Y≦3 --------------=Y-3 ,if Y>3 And...

I understand the concept of covariance, relating two complex random (scalar) variables. However, I get confused when I have both deterministic and random variables. Therefore, what I write might make very little sense -- I'm really only looking for any general advice on where to start reading...

Hi, I’m looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables. This would be easy if they were independent, but they’re not. There is a known correlation between...

Going over my Lecture Notes my Lecturer as Started with Show that a Gaussian Distribution Corresponds to a CTS random variable. Then she has i) Taken the f(x) = [p.d.f] and shown a) f(x) >= 0 for all x member of real numbers. b) Integral over all real numbers = 1 ii) Found the M.G.F then...

If you were to pick two random numbers on the interval [0,1], what is the probability that the sum of their squares is less than 1? That is, if you let Y_1 ~ U(0,1) and Y_2 ~ U(0,1), find P(Y_1^2 + Y^2_2 \leq 1). There is also a hint: the substitution u = 1 - y_1 may be helpful - look for a beta...

Hi all, I was having some troubles with a practise question and thought I'd ask here. Given an r.v. X has a pdf of f(x) = k(1-x2), where -1<x<1, I found k to be 3/4. And I found the c.d.f F(x) = 3/4 * (x - x3/3 + 2/3) Now I have to find a value a such that P(-a <= X <= a) = 0.95. I thought...

Homework Statement A random variable X has probability generating function gX(s) = (5-4s2)-1 Calculate P(X=3) and P(X=4) Homework Equations The Attempt at a Solution Ehh don't really know where to go with one... I know: gX(s) = E(sx) = Ʃ p(X=k)(sk) Nit sure how to proceed.. Any help would...

Homework Statement a) Let X1, X2, ...XN be a collection of independent Bernoulli random variables. What is the distribution of Y = \sumNi = 1 Xi b) Show E(Y) = np Homework Equations Bernoulli equations f(x) = px(1-p)1-x The Attempt at a Solution a)X1 + X2 + ... + XN = p...

Homework Statement If X and Y are independent uniformly distributed random variables between 0 and 1, what is the probability that X^2+Y^2 is less than or equal to one. Homework Equations P(Z<1) = P(X^2+Y^2<1) For z between 0 and 1, P(X^2<z) = P(X < √z) = √z The Attempt at a Solution...

Determine constant c so that random variable will have a t distribution? Homework Statement Suppose that five random variables x1, x2, x3, x4, x5 are independent and have normal distribution N(0,1). Determine a constant c such that the random variable c*(x1+x2)/\sqrt{x_3^2 + x_4^2 +...

Hello, I considered a statistically independent continuous random process f(x) such that Cov(f(x),f(y))=0 for x\neqy and Cov(f(x),f(x))=σ2. Then I would like to compute the correlation function of the Fourier transform of f, that is Cov\left( F(u),F(v)\right). The result I got from my...

Homework Statement The joint probability density function of the random variable (X, Y) is given by: f(x,y) = \frac{2x}{y^2} \text{where} \; 0 \leq x\leq 1 \; \text{and} \; y\geq 1 and 0 elsewhere. Find the probability density function of the folowing random variable: U=X+Y...