Random Definition and 1000 Threads

Homework Statement Let X ~ Exponential(3) and Y ~ Poisson(5). Assume X and Y are independent. Let Z = X + Y. Compute the Cov(X,Z).Homework Equations I know Cov(X, Z) = E(XZ) - E(X)E(Z). But how do I compute E(XZ) and E(Z) ?? Since for E(XZ), I would need the pdf/pmf (Exp is abs cts, while...

X and Y are independent, exponentially distributed random variables - with possibly different parameters Determine the density func. of Z = X / Y How to attack ?

I am creating a random combination(code) for a client. I need to see what the total number of combinations there can be. Please let me know if I am using the wrong word Combination vs Permutations. Formula: 2 letters + 2 numbers + 2 letters example: TR12FR The random letters are...

My professor made a rather concise statement in class, which sums to this: E(Y|X=xi) = constant. E(Y|X )= variable. Could anyone help me understand how the expectation is calculated for the second case? I understand that for different values of xi, we'll have different values for the...

I haven't studied quantum mechanics yet but I know that at the lowest level everything is random. But if everything is random how can we have definite laws like Newtons laws, electromagnetic laws. I mean if everything is random at the lower level these laws will also vary right, they can't be...

I've been eating organic food for the past year, and just recently I heard it's not any healthier for you. Is that true? I spend about 1/3 of my paycheck buying organic, it is really expensive and now I find out, that it's not any better for you. I just want to know if that's true?

Homework Statement 1000 independent rolls of a fair die will be made. Compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively. If the number 6 appears exactly 200 times, find the probability that the number 5 will appear less than 150...

Here is the question: Consider the experiment of rolling two tetrahedra that are unfair in the sense that each has the following probabilities for each of the four faces: P{1 dot}=1/10 P{2 dots}=2/10 P{3 dots}=3/10 P{4 dots}=4/10 Let X be the total of the outcomes in the two...

My problem is as follows (sorry, but the tags were giving me issues. I tried to make it as readable as possible): Let X have the pdf f(x)= θ * e-θx, 0 < x < ∞ Find pdf of Y = ex I've gone about this the way I normally do for these problems. I have G(y) = P(X < ln y) = ∫ θ * e-θx...

Homework Statement Hi guys, I'm absolutely desperate on the following problem: Consider a random walker who can make steps only to neighbor sites in "D" dimensions where D is an arbitrary natural number. Assume that the distance between 2 adjacent sites is the same for all sites and that the...

Homework Statement Let X,W,Y be iid with a common geometric density f_x(x)= p(1-p)^x for x nonnegative integer and p is in the interval (0,1) What is the characteristic function of A= X-2W+3Y ? Determine the family of the conditional distribution of X given X+W? Homework Equations...

Homework Statement f(x,y)= (4/5)(x+3y)exp(-x-2y) for x,y, >0 Find E[Y|X] Homework Equations E[Y|X] =integral y *f_xy (x,y)/ f_x (x) dy The Attempt at a Solution f_x (x) = integral [o,∞] [4/5](x+3y)exp(-x-2y) dx = (2x+3)/(5exp(x)) When taking the integral of y[(4/5)(x+3y)exp(-x-2y)] /...

Homework Statement let y_1 and y_2 be iid bin(5,1/4) random variables let v=y_1+2*y_2 and u = 3*y_1 -2y_2 find f_uv (u,v) and the cov(u,v) Homework Equations f_y (y) = (5 choose y) (1/4)^y (3/4)^5-x for x=0,1,2,3,4,5 covariance=E(uv)-E(u)E(v) The Attempt at a Solution...

Both the copper wire and the light bulb became hotter and hotter when a current was constantly passing through them, resulting in an increase in their resistances, which in turn lowering the value of the current through the conductor. (I did not allow time for both the wire and the light bulb to...

C++ or verilog or random process ?? I'm currently in 3rd year of my undergrad in Electronics & Communication engg. For my 6th semester, I'm required to take 1 elective from the following- -Data Structures with C++ -Random Process -Digital System Design using Verilog -Analog & Mixed mode VLSI...

Suppose that α and β are independently distributed random variables, with means; μ_α, μ_b and variances; δ_α^2, δ_β^2, respectively. Further, let c=αβ+e, where e is independently distributed from α and β with mean 0 and variance δ_e^2. Does it hold that E(αβ | c) = E(α|c)...

Work done so far... Integrating from 0 to infinity and equating it to 1, we get (c/2*10^-3) = 1 c= 2/1000 =0.002 Is it correct? http://www.chegg.com/homework-help/questions-and-answers/-q3136942#

In the last question in this link: http://pages.uoregon.edu/csinclai/teaching/Fall2009/files/hw8.pdf 1) I did not understand how they got the region for y1, y2, and y3... 2) How would the solution be different (or not possible) if X1, X2, and X3 were not iid? Thanks in advance

Hello, I'm studying the wave-particle duality, more specifically the matter-wave function of de Broglie: \Psi(x,t)=A sin 2\pi(\frac{x}{\lambda}-\nu t) where \lambda is the de Broglie wave-length and \nu is the frequency. The interpretation of this wave is that, \Psi^{2} would be the...

We have two independent random variables X and Y whose pdfs are given as f(x) and f(y). Now when you multiply X and Y you get a random variable say Z. Now what is the resulting pdf f(z)? I mean how is that related to the pdf of f(x) and f(y)? From what I read it looks like f(z)=f(x) *...

lets say that X is some random variable that takes +1 if rational otherwise -1. at http://tutorial.math.lamar.edu/Classes/CalcI/TheLimit.aspx in example 4, can we consider g(x) as a random variable because it's behaviour is same, right? is random variable really random or just function? I found...

I have the continuous random variable Y, defined such that: Y=3X+2 and the PDF of x is zero everywhere but: f(x)=\frac{1}{4}e^{\frac{-x}{4}}, x>0 I correctly got the mean like so: \mu=E(h(x))=\int^{\infty}_{0} h(x)f(x) and evaluated it to be 10. I am unsure as to how I go about...

I have always struggled in understanding probability theory, but since coming across the measure theoretic approach it seems so much simpler to grasp. I want to verify I have a couple basic things.So say we have a set χ. Together with a σ-algebra κ on χ, we can call (χ,κ) a measurable space...

hello physicsforum. i came here hopefully someone can answer this. heres what happend: i was out suing my camping stove. after i turn it off, and start packing it away, i shone the flashlight onto it and that's when i first discovered that there is a buzzing sound coming from it...

f(x) = 1/(1+x^{3/2}) x>0 how to generate such a random number?

I have conceptualized a method for generating serial binary data at rates varying randomly. This concept should be able to provide data at random rates with various characteristics.The most relevant application is generation of Random sensor data for testing C4I systems (Surveillance and...

Well I just read about whether mind can produce random numbers or not here. But that makes me wonder whether anything in this universe is random or not? I haven't yet studied quantum physics but I know that a lot in it is based on probability. So is anything truly random in this universe...

Suppose that I have n bits of random data. What is the probability that I can compress it by k bits? A colleague assures me that the largest possible fraction of random inputs that would compress by e.g. 32 bits would be 2^(-32). I am struggling to cope with this. I can see that if I have n...

Hi, I need your help, Say we have two random variables with some joint pdf f(x,y). How would I go about finding the pdf of their sum?

Hi there! I'm working on a random walk-problem my professor gave me. Given a MC with the following properties: P0,0 = 1 - p P0,1 = p Pi,i-1 = 1 - pi Pi,i+1 = pi i \in[1,∞) Xn: state at step number n The chain is irreducible and ergodic and 0 < p ≤ 1 introducing N: N = {min n...

Hi all, suppose I have a random discrete sequence like x= [1 2 3 2 5 2 4 2 3 1 6 3 5] (where possible outcomes are 1,2,3,4,5 or 6) and wanted to get its frequency distribution vector f=[2 4 3 1 2 1] which means frequency of occurrence of 1 is 2 times, 2 occurs 4 times , and so on. I...

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...