Random Definition and 1000 Threads

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...

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...

Let's say I have a very large number of objects with some property which is Normally distributed. If I choose a subset of these objects randomly, will those objects have the property Normally distributed too? If the answer is yes, can it be proven? Thanks

Generating a Random Number from an array for a blackjack simulator--Matlab I have a homework problem where I have to generate a single hand of blackjack to a player and allow the player to hit or hold. I'm ahving trouble generating the random card. My attempt: x =...

For a sum of two independent uniform discrete random variables, Z = X + Y, what is the probability mass function of Z? X and Y both take on values between 1 and L I know that for the sum of independent rv's the PMF is a convolution so... Ʃ(1/k)(1/n-k) from k = 1 to L but I'm wondering...

Homework Statement Two toys are started at the same time each with a different battery. The first battery has a lifetime that is exponentially distributed with mean 100 min; the second battery has a lifetime that is Rayleigh-distributed with a mean 100 minutes. a) Find the CDF to the time...

Homework Statement If Z has a standard gaussian distribution then what is the distribution of Z2 and what is its mean? The Attempt at a Solution Let T = Z2 Then we can get that pdf T = e-T/2(1+1/T) x (1/√(2∏T) I am not sure if this is correct and don't know how to find the...

for a random variable X with parameter λ, Y = m if m < X < m + 1 what is pmf of Y? it's basically asking for P[m< X < m+1] i know how to solve this for P[m < X < m + 1] ... it would be e-λm - e-λ(m+1) because P[a < X < b] = Fx(b) - Fx(a) and i know the PDF of an exponential random variable...

I am building an iPhone app where the iPhone is just going to sit on my desk measuring the distance to Earth's core. I will build a calibration function into my app to reduce the variation in the estimate. How, then, should I go about calibrating it?

Hi all I'm looking for solving this problem to find the closed form solution if it is possible: Y=\frac{1}{X} Where X is uniform random variable > 0 I know the expected value for X which is \overline{X} is there a method to find the expected value of Y which is \overline{Y} in term of...

Hey, I have a pdf of a random variable Z given. I am being asked to calculate what the moment generating function of a r.v Y= Z + c will be where c is a constant in ℝ I tried to calculate it in the following way: \int^∞_0 e^{(z+c)t} f(z+c)dz where f(z) is an exponential pdf with...

Hi all: Now I have a question about the concept of diffusion coefficient in two cases: the diffusion equation (J=DdT/dx) and the random walk (tao^2=6Dt). My quesion is the two D in two equations are the same or different. If they are different, is there any relationship between them? Best Xu

I have a masters degree in probability and statistics but am new to quantum physics. I have been reading an elementary text about the Schroedinger equation and I keep thinking that the Heisenberg Uncertainty Principle could emerge from a random walk that has the characteristic that as the...

For X ~ N(μ, σ), what is P[|X-μ] < σ] in terms of the Q function? I know that P[|X-μ] < σ] can be decomposed into P[X > -σ + μ] + P[X < σ + μ] I'm not sure what to do next. i know P[X < σ + μ] can be expressed as 1 - phi(σ + μ - μ / σ) = Q(1), but I'm not sure how to approach P[X > -σ + μ]. I...

Let X and Y be independent and uniform on {1, 2, ... M} Find P(X > Y) so i know that P(X = x) = 1/M and P(Y = y) = 1/M i don't understand how Find P(X > Y) = (M+1)/2M

Homework Statement Write a program that takes a positive integer N and a string as command line arguments (N is assumed to be smaller than the length of the string). The program should pick N random characters from the string and construct and print a new string composed of these random...

Homework Statement X, Y, (X_n)_{n>0} \text{ and } (Y_n)_{n>0} are random variables. Show that if X_n \xrightarrow{\text{P}} X and Y_n \xrightarrow{\text{P}} Y then X_n + Y_n \xrightarrow{\text{P}} X + Y Homework Equations If X_n \xrightarrow{\text{P}} X then...

Hi, I am confused with the results of a seemingly simple simulation that is generating a log normally distributed output. Please see the attached results file. Simulation: I have built a Scratch program that randomly picks six letters from a group of six letters (A, B, C, D, E & E). The...

Homework Statement The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 70000 miles and a standard deviation of 5000 miles. A: What is the probability that...

Homework Statement Suppose X1 , X2 , . . . , Xn are independent random variables, with common expectation μ and variance σ^2 . Let Sn = X1 + X2 + · · · + Xn . Find the variance of Sn. The attempt at a solution Expected value: E[S_n] = n E[X_i] = n\mu \hspace{10 cm} (1)...

Hello and thank you in advance for anyone taking time to respond. I working on formulating a theory for elastodynamics, but my statistics is admittedly weak. I'm trying to find a relationship between a non random function and a random function, for example, the covariance. <A(x)B(y)>=some...

Hi. I choose randomly a one word, and I decided to choose a word blue. Let random variable x be a length of the word blue. What is expected value and variance of a word blue? So, random variable x = 4. E(X) = [SIZE="5"]Ʃ xi fX(xi) i:xi∈S x1 + x2 + x3 + x4 = 10...

The random variable X assumes the values 1,2,3 and 4 with equal probability. Find the density functions of the following variates: Attempted solutions: X 1 2 3 4 Pr(X) 1/4 1/4 1/4 1/4 a) Y=1-2X Y -1 -3 -5 -7 Pr(Y) 1/4 1/4 1/4 1/4 b) Z= X/(X+1) Z...

Hello all! So if I wanted to make and order a part to a device I am designing, where would I go to do that? I know this may seem like a weird question but here is my situation. My brother has two graphics cards in his computer and there is a VERY thin space between them, and because of that...

Let X be a discrete random variable that can assume the values -1, 0,1,2,3,4 with the probabilities 1/6, 1/12, 1/6, 1/4, 1/12, 1/4. Find the probability densities of the following random variables: a) Z= X^2 + 1 h(y)= f(g^-1(y)) Attempted Solution X= -1 0 1 2 3 4 Z=...

Some metals generate electrons when photons hit them, If so then what direction will the electron go into, will it be random and the uncertainty principle and quantum randomness. Or will it go in a direction relative to the point of impact from the photon, So if you shot a photon at an atom...

Ok, since nobody answered my last problem, I simplify. :) Let Z = γ1X1 + γ2X2, where the gammas are just constants p(Z) = exp(Z)/(1 + exp(Z)) X1 and X2 are bivariate normal and put Y = α + β1X1 + β2X2 + ε where ε ~ N(0,σ). Now, we want to find f(p(Z)|X1,Y). In this case, is it legal...

Distribution of difference of two second degree non central chi squared random variables. This problem can be cast as an indefinite quadratic form for which there are a number of general numerical techniques to determine the CDF. Alternatively, it may be written as a linear combination of...

Hi guys, I'm doing some thinking about random walk. Imagine there is a bounded 2D plane and a single spawn point. The spawn produces units which must bring in minerals scattered around the spawn. The locations of minerals are not known, so the units diffuse randomly away from the spawn...

I know this probably isn't the best place to ask this question but here goes anyways lol What's wrong with the next sentence/ "What do you feel when you see a smoke detector? Do you ever feel like an astronaut? No? Well, the next time you see one, try to imagine that it's part of your...

Homework Statement 1) Let X have the p.d.f f(x) = 3(1-x)2, 0≤x<1. Compute: a) P(0.1 < X < 0.5) etc... 2) Find the mean and variance, and determine the 90th percentile , of each of the distributions given by the following densities: a) f(x) 2x, 0≤0<0 etc.. 3) Find the 50th...

Hello, I am a student in high school and I possesses a keen proclivity for mathematics and physics. A contentious topic of discussion has come up among my friends, and I seek some assistance in resolving it. A few days ago in my AP Chemistry class, the instructor told us that were we to...

attached in a file. I will be grateful for some help here. Thanks :smile:

Using Mathematica, I need to define a discrete probability distribution of N equally spaced angles on the interval [0, 2Pi], which isn't exactly uniform. More precisely, I need the distribution to feature a "Poisson-like" behavior : the angles should be randomly selected by random "packs"...

Everyone knows that particle-antiparticle pairs are supposed to be able to spontaneously pop into existence from "nothing", exist whilst the uncertainty principle allows it, then recombine and annihilate. Is it really spontaneous though, or has any thought been given towards whether this is...

For the density function for random variable Y: f(y) = cy^2 for 0<= y <= 2; 0 elsewhere We are asked to find the value of c. I did a definite integral from 0 to 2 of cy^2. I get c = 3/8. Why would the book show an answer of c = 1/8? Is this an error on their part or am I missing something...

Homework Statement D = (L + E) / S Where L, E, and S are mutually independent random variables that are each normally distributed. I need to find (symbolically), the conditional PDF f(d|s). Homework Equations The Attempt at a Solution Not sure what to do with so many...

Data is collected on the number of fish caught per day on a month long fishing expedition. It is hypothesised that the data are consistent with a negative Binomial random variable ,X , starting at 0, so that X~Neg Bin(k,p) where E[X]=k(1-p)/p and Var =k(1-p)/p^2 . However, before a hypothesis...

Hello everyone! I am stuck in my research with a probability density function problem.. I have 'Alpha' which is a random variable from 0-180. Alpha has a uniform pdf equal to 1/180. Now, 'Phi' is a function of 'Alpha' and the relation is given by, Phi = (-0.000001274370471*Alpha^4) +...

I am stuck on the following problem: Five items are to be sampled from a large lot of samples. The inspector doesn't know that three of the five sampled items are defective. They will be tested in randomly selected order until a defective item is found, at which point the entire lot is...

A friend and I had an interesting thought and would like to know if it has any consequences. It is a well known fact that a time-varying electric field is non-conservative, it has a time-dependent Hamiltonian, blah, blah, blah, blah. I'll give this a standard treatment to set up the punchline...

This is actually for a program, but the challenging part is really the math. So you're given a number 0, 1, 2, or 3 and the probability of getting each is the same. Now given this random number, I need to output a number 0, 1, 2, 3, 4, 5, or 6 but the probability of getting each number needs to...