Random Definition and 996 Threads

Homework Statement A trial consists of throwing two dice. The result is counted as successful if the sum of the outcomes is 12. What is the probability that the number of successes in 36 such trials is greater than one? What is this probability if we approximate its value using the Poisson...

Can someone tell me why this random function is not random? I copied it exactly from my textbook, however, it only generates a "3", rather than a random number (1, 2, or 3). int randomMove ()//generates a random move for player 2 { int x = rand () % 3 + 1; return x; } int...

Hi everybody, i didn't wanted to create two separate threads so merged them into one. i got confused watching Brian Green explaining QM on one of his shows. He compared distribution in double slit experiments with throwing a ball on a roulette. He said that casino doesn't have to know...

Spice http://www.kia-glitz.com/wp-content/uploads/2012/12/Spice-Watching.jpg Staring wistfully out the window into the night http://www.kia-glitz.com/wp-content/uploads/2012/12/Spice-CloseUp2.jpg Isn’t he just adorable? Pepper...

In the page that I attached, it says "...while at the continuity points x of F_x (i.e., x \not= 0), lim F_{X_n}(x) = F_X(x)." But we know that the graph of F_X(x) is a straight line y=0, with only x=0 at y=1, right? But then all the points to the right of zero should not be equal to the limit of...

1. In scanning electron microscopy photography, a specimen is placed in a vacuum chamber and scanned by an electron beam. Secondary electrons emitted from the specimen are collected by a detector and an image is displayed on a cathode-ray tube. This image is photographed. In the past a 4- ...

Homework Statement A binary information source produces 0 and 1 with equal probability. The output of the source, denoted as X, is transmitted via an additive white Gaussian noise (AWGN) channel. The output of the channel, denoted as Y, satisfies Y = X + N, where the random noise N has the...

Fortran's Random numbers! Hi everyone! I have a doubt about random numbers on Fortran: how does the computer choose random numbers? Why don't they change each time I run the programme? Are they really random then? Thanks!

Hello everyone! I'm looking at the following random variables: $Z_1$ is normally distributed with zero mean and variance $\sigma _1 ^2$ $Z_2$ is normally distributed with zero mean and variance $\sigma _2 ^2$ $B$ is Bernoulli with probability of success $p$. $X$ is a random variable that...

I have a non-increasing sequence of random variables \{Y_n\} which is bounded below by a constant c, \forall \omega \in \Omega. i.e \forall \omega \in \Omega, Y_n \geq c, \forall n. Is it true that the sequence will converge to c almost surely? Thanks

[FONT=Courier]Classify the following as discrete or continuous random variables. [FONT=Courier] [FONT=Courier](A) The number of people in India [FONT=Courier](B) The time it takes to overhaul an engine [FONT=Courier](C) The blood pressures of patients admitted to a hospital in one day...

Hey guys, I need to fill up a box with uniformly distributed set of non-overlapping spheres. This is quite easy to do numerically. I was wondering what is expectation value for the asymptotic volume fraction of the spheres. Suppose I have a big box with side L, and spheres with radius R<<L. I...

Consider continuous function x(t), which has zero time average: \lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{T/2} x(t)\,dt = 0 and exponentially decaying autocorrelation function: \lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{T/2} x(t)x(t-\tau)\,dt = C_0e^{-\gamma |\tau|}...

I have the random process: Sequence 1: 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 ... Sequence 2: 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 ... Sequence 3: 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 ... where let nature choose one of these sequences at random with equal probability 1/3. Can we say anything about this...

Hey! I am studying group theory for particle physicists right now and I came across the following general question (Tell me if you think this rather belongs to the homework section, I am new here.) Say I am given a set of matrices which represent the generators of an algebra, but I don't know...

I choose a random number p_1 \in [0,1) and a subsequent series of (increasingly smaller) random numbers p_i \in [0, p_{i-1}). Then I can calculate the sum \sum_{i=1}^\infty p_i. Naturally, this sum is dependent on the random numbers chosen, so its particular result is not very insightful...

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...

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

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 happened: 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...