Random Definition and 996 Threads

We studied random walk starting from a probability conservation : p(x,t)=p(x+dx,t+dt)+p(x-dx,t+dt) Which means the particle can go left or right by dx in time dt. The solution of the differential equation starting from a delta is a gaussian, which means the particle could go apparently at...

Well, not quite a random walk. The steps aren't necessarily ±1, but they have mean 0 and will take values >ε with positive probability. It seems intuitive that such a process will be unbounded and will cross this bound infinitely many times (in 1D). Does anyone know of a result that says this?

Question already asked on http://math.stackexchange.com/questions/1310194/confusion-about-a-random-process?noredirect=1#comment2661260_1310194, but couldn't get an answer so reposting here...

Homework Statement Random variable x is defined on interval (1,3) and it has probability mass function f(x) =A(x2 +1= a) Find PMF, g(y) for y=x2 b)Expectation of y c)Variance of y d)Distribution function of y. e)most probable value of y The Attempt at a Solution As far as a), i integrated from...

Does the energy of the electron in a random hydrogen atom is in superposition of all eigenvalues(some value upon measurement) or you will find it most likely in the ground state. Additional clarification: From my reading the textbooks said the electron energy is in superposition, yet the...

In a recent thread I posted there was mention of evolution having a specific sense in biology. I just spent an hour reading some evolution primers and I think I have a better sense of how this works at the molecular level but will need to read a lot more till it all hangs together in my mind...

http://news.nationalgeographic.com/2015/05/150315-quadruple-quasar-mystery-space-astronomy/National Geographic quoting Dr Hennawi, the lead author of the Science paper, says it is a ten million to one chance to find four quasars so close together. How much more unusual is it that in the first...

Hi. I am trying to create a program that I will give the maximum range (1,...,max) from which to generate random numbers, and make it generate N=maxgen random numbers (which later I can use for example in another program). Below you can see the code I wrote: #include <iostream> #include <ctime>...

Hi, I'd like to ask you if is there (in universe) anything random - any event which hasn't a reason. I say no but I haven't enough knowledge about physics so perhaps there are some things I don't know. Thank you

The title sums up my question: Is the quantum world truly random? If so, doesn't this seem to contradict a primary assumption of science, determinism? How is it that something can truly be random? Are there any theories that deal with this? By this I mean to ask if there are any theories that...

Homework Statement Find the probability distribution for a random walk on a d-dimensional lattice.[/B]Homework Equations [/B]The Attempt at a Solution I'm trying to find the probability distribution for a random walk on a lattice with lattice constant a in arbitrary dimension d. The rules...

Homework Statement The problem is relatively simple. I am modelling mass diffusion, and that's going well, but she has offered extra credit if we can write the problem without using any if-statements. In a clutch my plan is fall back on a Case Statement and pull barracks-lawyer and insist...

Hello, want to know if it's correct 1. Homework Statement X and Y two random variables iid of common density f and f(x)=x*exp(-x²/2) if x≥0 and f(x)=0 if x≤0 and Z=min(X,Y) Find -The density of Z -The density of Z² - E[Z²] Homework EquationsThe Attempt at a Solution 1.[/B] FZ(u) = P(min(X,Y...

Hi, I'm trying to solve this exercise but I really don't know how 1. Homework Statement Let X1, X2,.. be a sequence of iid random variables following a uniform distribution on (0,1). Define the random variable N≥2 as the first point in which the sequence (X1,X2,...) stops decreasing. i.e If...

Hello guys, I have a sample of about 400 natural numbers though I can get more numbers. To give you an idea the mean and the standard deviation are 29038031 and 1842882 respectively and I expect the numbers to follow a Gaussian distribution. I'd like to perform a test to tell me the probability...

What textbooks would you recommend for self studying Nonlinear Dynamics? I am a undergraduate junior who will be doing research on nonlinearity of spiking neurons. I have taken courses on ODE, vector calculus, probability, statistics, and linear algebra.

An issue I’ll call Issue 1 arose and prompted Event A to occur. A few days after Event A occurred, I received a virus email I’ll call Virus Email 1. The content of Virus Email 1 referred to something that is a direct outcome of Event A. Therefore, Virus Email 1 is directly related to Event A...

Assume I have an ideal laser pointing which light will always move parallel to where the laser pointer is pointing. This mean that no matter how far I stand away from the laser pointer, I will see the same spot of light with the same light and intensity. In that case is it possible to determine...

I was trying to understand Bells theorem and I found this site http://www.upscale.utoronto.ca/PVB/Harrison/BellsTheorem/Analogy.html easy to understand. I found the "The Second Analogy: More Boxes" in it easy to grasp. But one thing I didn't understand in it, where it uses the word random...

Homework Statement In a study to estimate the proportion of residents in a city that support the construction of a new bypass road in the vicinity, a random sample of 2025 residents were polled. Let X denote the number in the sample who supported the proposal. To estimate the true proportion in...

Homework Statement Let ##X## be a random variable such that ##\mu_X = 0## and ##K_{XX} = I##. Find ##Cov(a^T X, b^T X)## for ##a = (1, 1, 0, 0)## and ##b = (0, 1, 1, 0)##. The Attempt at a Solution I guess I am assuming that ##X## is a 4 element random vector. I can't know values of the random...

Given the PDF: f(x) = 1/12 , 0 < x <= 3 x/18, 3 < x <= 6 0, otherwise find the expected value, E(x). I know how to find the expected value if there was only one interval, but don't how to do it for two.

Hi, So I'm writing a programme in Fortran95 atm and I want to produce an array of 1s and 0s. I've used a random number and random seed generator to produce 10 numbers between 0 and 1 and I want to use a NINT statement to round these random numbers to 0 or 1. However when I try this the...

So I wanted to get some second opinions on this situation I have thinking about.Lets say an electron enters, normally, a section of bfield that is perpendicular to its motion such that the electron will undergo circular motion. This is the simple part and is labeled as "E0" in the picture...

Homework Statement Suppose that A, B, C are independent random variables, each being uniformly distributed over (0, 1). ) What is the probability that all the roots of the equation Ax2 + Bx + C = 0 are real? Homework Equations (b) What is the probability that all the roots of the equation...

Homework Statement Let X be a random variable with the following probability distribution X 0 1 2 3 4 f(x) 1/16 1/4 3/8 1/4 1/16 If another random variable Y = X^2 + 1 is formed, find the mean E[Y]. 2. Relevant equation...

Sorry didn't look too deep into it but had a random thought (and a couple drinks) ; would it be plausible to generate power by harnessing angular momentum from passing molecules? Perhaps hydro and wind generators could get an efficiency boost?

Hi all, I understand Genetic algorithms aside form why crossover helps things, it has no guarantee of getting the best characteristics of each chromosome. Ie say you had a genetic algorithm to calculate square roots, fitness = 1(Abs(NumToFindRoot of-(Guess*Guess)) and your guess was a binary...

How we are able to recollect things and how random thoughts are generated in our mind? Is there any specific reason? As I can't edit my thread title, as I realize the topic should have been How random thoughts come to our mind?

I am trying to use a generated random sample in R to estimate the mean and variance for a Poisson random variable. The first one is a Poisson random variable with mean 5. To estimate the above I generate a random sample in R with the following code: P5 <- rpois(100,5) Given the above I want to...

hi I read an article about stochastic error modeling, and I didn't understand this extract about error sources : how can the "rate random walk" be present, while the gyroscope directly angular rate ? the article's title is : "Stochastic Modeling of MEMS Inertial Sensors " by Petko Petkov and...

Labeling + or - on random point on circuit- What does it mean in this link? http://i.imgur.com/ECSDONZ.png I also have an unrelated question but the topic is similar enough that I thought I would not create another thread. Why is the meaning and use of labeling + and - on resistors? I...

I'm new to the electrical engineering field and need guidance on how I can program a PIC (PIC12F675P) controller to generate random high/low frequency noises through a amplifier (TDA2822M). The sounds I'm aiming for need to be similar to those generated by a dial up modem. I will appreciate...

Homework Statement If Y=X1+X2+...+XN prove that <Y>=<X1>+<X2>+...+<XN> Homework Equations <Y>=∫YP(Y)dY over all Y. The Attempt at a Solution I only seem to be able to show this if the Xi are independent, and I also think my proof may be very wrong. I basically have said that we can write the...

Homework Statement Z = X - Y and I'm trying to find the PDF of Z. Homework Equations Convolution The Attempt at a Solution Started by finding the CDF: Fz(z) = P(Z ≤ z) P(X - Y ≤ z) So I drew a picture So then should Fz(z) be: since, from my graph, it looks as though Y can go from...

Does anyone know where I can go to figure out how to generate a random 3-4 letter sequence BUT with every click that sequence is stored in an array and can not come up again?

Homework Statement Let X denote a continuous random variable with probability density function f(x) = kx3/15 for 1≤X≤2. Determine the value of the constant k. Homework Equations I'm not sure if this is right but I think ∫kx3/15 dx=1 with the parameters being between 2 and 1, The Attempt at a...

Homework Statement If X is uniformly distributed over (0,1), find the PDF of Y = |X| and Z = e^X Focusing on the |X| one Homework Equations Derivative of CDF is the PDF The Attempt at a Solution So I start by writing down the CDF of X, Fx(x): 0 for x <0 x for 0 ≤ x ≤ 1 1 for x ≥ 1 And I...

Homework Statement Here's the problem with the solution provided: Homework Equations Fundamental Theorem of Calculus (FToC) The Attempt at a Solution So I understand everything up to where I need to take the derivative of the integral(s). Couple of things I know is that the derivative of...

Homework Statement If ##X\sim\mathcal{U}(-1,1)## and ##Y = X^2##, is it possible to determine to ##cov(X, Y)##? Homework Equations \begin{align} f_x &= \begin{cases} 1/2, & -1<x<1\\ 0, & \text{otherwise} \end{cases}\\ f_y &= \begin{cases} 1/\sqrt{y}, & 0<x<1\\ 0, & \text{otherwise} \end{cases}...

We have a r.v. X with p.d.f. = sqrt(θ/πx)*exp(-xθ) , x>0 and θ a positive parameter. We are required to show that 2 θX has a x^2 distribution with 1 d.f. and deduce that, if x_1,……,x_n are independent r.v. with this p.d.f., then 2θ∑_(i=1)^n▒x_ι has a chi-squared distribution with n...

If one has a Bernoulli random variable W that is derived from a Variable T (Poisson λ), by the following rules W = (if T=0 then W=1 and if T>0 then W=0), I am having trouble finding the pf for W. Any suggestions about how to proceed forward?

So, I have a jokester (MHB user Cmoney) in my class (what teacher doesn't?), who decided to go all-out on a quiz question. The question reads as follows: You are planning a report on apartment living in a college town. You decide to select three apartment complexes at random for in-depth...

Homework Statement The components of a random vector ##\mathbf{X} = [X_1, X_2, \ldots, X_N]^{\intercal}## all have the same mean ##E_X[X]## and the same variance ##var(X)##. The "sample mean" random variable $$ \bar{X} = \frac{1}{N}\sum_{i = 1}^NX_i $$ is formed. If the ##X_i##'s are...

Hi, I am having a hard time understanding why the Addition Rule for two Random Variables holds even when the random variables are dependent. Essentially: why is E(X+Y) = E(X) + E(Y) when X and Y are dependent random variable? Given the two variables are dependent, if X happens to take on a...

Hi all I am doing this question right now and I don't even know how to start it up. I know that it's in relation to a sum of a random number of random variables, but I don't know how to continue on from that. I've read my textbook and it states some definition for an MGF which is: $M_{y}(t) =...

Homework Statement Determine the minimum mean square error for the joint PMF. You will need to evaluate ##E_{X, Y}[(Y - 14/11\cdot X - 1/11)^2]##. Homework EquationsThe Attempt at a Solution The answer is ##\frac{3}{22}##, but when I work it out, I get ##\frac{203}{484}##. From my values, I...

With a Poission random variable, we know that \(E[X] = var(X) = \lambda\). By definition of the variance, we can the second moment to be \[ var(x) = E[X^2] - E^2[X]\Rightarrow E[X^2] = var(X) + E^2[X] = \lambda(1 + \lambda). \] The characteristic equation for the Poisson distribution is...

The discrete random variable K has the following PMF: p(k) = { 1/6 if k=0 2/6 if k=1 3/6 if k=2 0 otherwise } Let Y = 1/(1+K), find the PMF of Y My attempt: So, I am really confused about what this is asking. I took...

Homework Statement A standard procedure for finding an approximate mean and variance of a function of a variable is to use a Taylor Expansion for the function about the mean of the variable. Suppose the variable is y, and that its mean and standard deviation are "u" and "o". f(y) = f(u) +...