Random Definition and 1000 Threads

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, Here's a particular procedure to deal with the giant component of a random graph. Is it "almost always" as efficient as experiments suggest? If so, can you shed some light as to how the giant component evolves under this procedure? Suppose we're given a large graph with a large...

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...

The gold standard for generating random numbers is the quantum effect of nuclear decay -- particles and photons being emitted from the atomic nucleus -- and unless you are one of those Hidden Variables types this is really random. The silver standard is thermal noise. There is a nice article in...

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 Given f(x,y) = x + y 0≤x≤1, 0≤y≤1 zero , otherwise Show that X+Y has density f(z) = z^2, 0 < z < 1, and z(2-z), 1 < z < 2. Homework Equations Also, how to find the density f(z) for X*Y? The Attempt at a Solution Even if f(z) is not given, some...

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...

Hi, I am stuck with the problem of solving this problem for my research. I have 3 random variables say X, Y, and Z and say Pr[X > Y] = p_xy, Pr[X > Z] = p_xz, and Pr[Y > Z] = 0.5. Note that p_yx = 1 - p_xy. Similarly, p_zx = 1 - p_xz, p_yz = p_zy = 0.5 I need to find out the Pr[X >...

Hi All, I'm hoping I can find some help to solve a puzzle that came up last night with friends. I thought I could find a solution but have been out of college too long. We had 3 couples over (8 adults), and wanted to play a single round for each possible pairing of the 8 people. After playing...

Hello Everyone, The following is a subproblem of research project I'm working on, i.e. not a homework. Let's suppose you have a bounded 2d plane and n distinct probes that do random-walk in that plane. The world is closed in a sense that a probe going outside the border ends up being on the...

if X1 and X2 are two uniformly distributed random variables and if Y = X1 + X2 why is that the probability density function of Y is convolution of probability density functions of X1 and X2 ? I tried many ways, I'm not able to get at this conclusion

Homework Statement Given a random variable X with a known distribution (e.g. a beta distribution), find the distribution of f(X) = X^2 + X The Attempt at a Solution I've tried the normal approaches: the standard transformation theorem; conditioning on X; Laplace transformation, etc...

import java.awt.Color; public class ChangingColor { public static void main(String[] args) { while (true) { int R = (int) (Math.random() * 256); int G = (int) (Math.random() * 256); int B = (int) (Math.random() * 256); Color randomColor = new Color(R, G, B)...

I've made a 2D walker to compare different RNG's. I'm measuring the succes of each walk as the distance from the origin to the endpoint, using the regular 2-norm. The thing I can't seem to work out is the variance. D_n=\sqrt(x_n^2+y_n^2) Var(D_n)=E[D_n^2]=E[Z_1^2+...+Z_n^2] Since...

Hi all, Could you please answer my following question related to an exponential random variable? Thank you. Let X represent the waiting times at a telephone in an office. Assume that X is an exponential random variable with parameter λ: P(X < t) = 1 - e^{-λ*t} At each time when the...

Can something random occur in the sense that no factors are involved of it happening? I would think that nothing random can occur, if a photon goes a special way, then it's determined by factors and events prior to the photon "choosing" it's way, or am I wrong? If there are any articles or...

Hello! I am writing because I recently became interested in probability distributions, and I have to you a few questions. Poisson distribution is given as a probability: f(k;\lambda)=\frac{\lambda^{k}e^{-\lambda}}{k!} But what is lambda? Suppose that we consider as an unrelated incident...

Hello, I have a really tough time understanding this concept although this isn't anything more complex than a composition of functions. I have a done example from my book that I am trying to interpret. p_\xi (x)=\frac{1}{\pi} for an interval between [0,∏] The...