Random Definition and 1000 Threads

I was looking out for dedicated true random number generators and was surprised that there seem to be only very few around on the market. Anyone has experience here?

Hi there, In Office Excel 2013 - If I make a list of five statements, each in a separate cell but within the same column, in another cell how can I get Excel to randomly select three of those statements? Not sure how to write the =RAND() equation. Any help will be much appreciated, Stevie

Are they always independent from each other so that you can multiply their E[X] together to form another E[X] with the same distribution and pmf or pdf?

Hi, I'm an economics graduate student doing some work on a nested logit model. I am trying to generate random variables that follow the following CDF: F(x_1, x_2) =\textrm{exp}[ -(e^{-2x_1}+e^{-2x_2}) ^{1/2}] (This is an extreme-value distribution) With a single random variable, I...

I think I just had the weirdest dinner ever. My wife invited her secretary and the secretary's girlfriend to dinner, and of course made me go with her. The only thing I knew before showing up to dinner is that her name was Kelsey. Well, we showed up early and sat at the table. My wife left...

Homework Statement Given a sequence of independent random variables {X_n}, each one with distribution Exp(1). Show that Y_n = \displaystyle\frac{X_n}{\log(n)} with n \geq 2 converges to 0 in probability but it doesn't coverges almost surely to 0. Homework Equations Density for each X_n...

Homework Statement A man wants to travel to four cities (A,B,C,D) but he has such a bad memory that he can't remember the cities that visited, therefore, if he travel to city A he can choose between (B,C,D) and if he then travel to B he can choose between (A,C,D). Find v, If v it's the...

Hi all, I would like to find the distribution (CDF or PDF) of a random variable Y, which is written as Y=X_1*X_2*...X_N/(X_1+X_2+...X_N)^N. X_1, X_2,...X_N are N i.i.d. random variables and we know they have the same PDF f_X(x). I know this can be solved by change of variables technique and...

I am trying to learn MATLAB with MIT OCW and I am running into some trouble. It says as an assignment: c. cMat = a 10x10 matrix where the vector 1:100 runs down the columns (use reshape). so 1 11 21...91 2....92 . ..... 10...100 is the matrix I am trying to make and another...

hello! I'm trying to understand the following property: Let X and Y be independent random variables z: = X + Y. Then http://imageshack.us/a/img268/9228/71pe.png where fZ (z) is the probability mass function for a discrete random variable defined as follows...

Human being's can't take exact random samples from continuous distributions like the uniform distribution on [0,1]. If we attempt to make measurements of physical pheonomena, we are limited to finite precision. Hence it isn't possible do empirical tests of properties involving exact sample...

If X is a continuous random variable and g is a continuous function defined on X (Ω), then Y = g(X ) is a continuous random variable. Prove or disprove it.

If X is a random variable distributed uniformly in [0, Y], where Y is geometric with mean alpha. i) Is this definition valid for uniform distribution ? ii) If it is valid, what is the pdf of the transformation Y-X?

Given that an Poisson arrival has occurred in an interval [0,t], where t is geometric with mean (alpha). Is it true that the arrival instant is uniform in [0,t]?

In the Cosmic Landscape, Susskind writes: My question is if subatomic movements are random then does the conservation of momentum law break down at the quantum level? My hunch is yes. The conservation laws only apply at the classical level. Some people say that Noether's Theorem proves...

Hi all! I have no application in mind for the following question but it find it curious to think about: Say that we have a square matrix where the sum of the elements in each row and each column is zero. Clearly such a matrix is singular. Suppose that no row or column of the matrix is the...

I'm having a bit of a problem proving the second condition for a martingale, the discrete time branching process Z(n)=X(n)/m^n, where m is the mean number of offspring per individual and X(n) is the size of the nth generation. I have E[z(n)]=E[x(n)]/m^n=m^n/m^n (from definition E[X^n]=m^n) =...

the random variables X1,X2... are independent and they take 0 and 1 values and they have expected value 0 if we have Y=X1+X2+...+Xn and Z=X1+X2+...+Xn+Xn+1 what is the ρ(Y,Z) for n=46 i know that ρ(Y,Z)=cov(Y,Z)/(sqrt(var(Y)*sqrt(var(Z)) but i need some help on how to find the cov and vars...

Hi, Let's say I'm given X and Y identical independant continuous random variables. We pose Z =X/Y, I remember there is a way to find the density function of Z, altough I can't get to remember how to do it and my probability book is out of town.(And I'm not so sure what to look for in google)...

I'm looking for an analytical solution to a very simple problem I've come across. Start with a circle of radius a. Now place n points at random positions inside this circle. Can you calculate the expectation value for the mean distance between the points? For the sake of argument can you...

I'm thinking about how to do a proof that a computer cannot generate a truly random number. Attempt. Let Ω = {ω1, ω2, ..., ωn}, a subset of ℝ, be all the numbers represented on a certain machine. A random number generator [FONT="Century Gothic"]rand(), because its output is dependent on how...

Hi all, I'm trying to self-learn about chaos, fractal, or anything that correspondence to random analysis (maybe with some material from statistical physics). Anyone know what the best textbook for these fields?

Problem statement: Define the random process X(t) = C where C is uniform over [-5,5]. a) Sketch a few sample realizations I need reassurance that if I do a a few sample realizations of this random process they are all going to look the same. They are going to be an horizontal line with...

Hello. I have a problem with probability theory task. The task is: X and Y is independent random variables with same density function fx=fy=f. What will be probability of P(X>Y). This P(X>Y) reminds me a cdf: P(X>Y)=1-P(X<Y)=1-cdf of X. Cdf of x is equal to integral ∫f dx from -inf to...

Random walk or binomial?? Statement: A drunk person wonders aimlessly along a path by going forward 1 step and backward 1 step with equal probabilities of ½. After 10 steps, a) what is the probability that he has moved 2 steps forward? b) What is the probability that he will make it to his...

Statement: A drunk person wonders aimlessly along a path by going forward 1 step and backward 1 step with equal probabilities of ½. After 10 steps, a) what is the probability that he has moved 2 steps forward? b) What is the probability that he will make it to his front door within 20 steps...

Hello all, I have the following continuous-time random process: v(t)=\sum_{k=0}^{K-1}\alpha_k(t)d_k+w(t) where d_k are i.i.d. random variables with zero mean and variance 1, alpha_k(t) is given, and w(t) is additive white Gaussian process of zero-mean and variance N_0. Can we say...

Let x(1),...,x(N) all be independent uniformally distributed variables defined on (0,1), i.e. (x(1),...,x(N)) - U(0,1). Define the random variable y(i) = x(i)/(x(1)+...+x(N)) for all i=1,...,N. I’m looking for the pdf of the random variables y(1),…,y(N). Has anyone come across such random...

Problem: Suppose that $X \text{ ~ Exp}(\lambda)$ and denote its distribution function by $F$. What is the distribution of $Y=F(X)$? My attempt: First off, I'm assuming this is asking for the CDF of $Y$. Sometimes it's not clear what terminology refers to the PDF or the CDF for me. $P[Y \le y]=...

This is something that when I see the work done it makes sense, but I find it difficult to do myself. I'm also aware there is an explicit formula for doing this but that involves Jacobians and a well-defined inverse, so I think it's more intuitive to do it step-by-step. Problem: Suppose $X...

Professor Roberto has to take an oral examination. The grading scale is as follows: 5: = best and 1: = worst. At most he only gives the note 4. Each student under review is questioned if he is a Lakers fan. The student's grade is based on his answer (is a fan / not a fan) and on the language in...

Homework Statement We have two independent, exponentially distributed random variables X and Y (with parameter a). Z = X/(X+Y) What is Z:s distributon function? Homework Equations The Attempt at a Solution I think I need some intuition to what I'm really doing with these, I'm having a...

Homework Statement X is uniformly distributed over [-1,1]. Compute the density function f(y) of Y = 2X2 + 1. Homework Equations The Attempt at a Solution FY(Y) = P(Y < y) = P(2X2 + 1 < y) = P(X < +\sqrt{1/2(y-1)} = FX(+\sqrt{1/2(y-1)}) We have that f(x) = 0.5 for -1 < x <...

Homework Statement Find correlation between random variables x and y in the following: $$P_{x,y}(x,y)=A \ xy \ e^{-(x^2)}e^{-\frac{y^2}{2}}u(x)u(y)$$ Homework Equations The co-variance ##\sigma_{xy}=\overline{(x-\bar{x})(y-\bar{y})}## or ##\sigma_{xy}=\overline{xy}-\bar{x}\bar{y}##...

I didn't post this in the probability section cause the questions I have are more regarded to communication system engineering. I haven't actually been able to wrap my head around these concepts mainly cause all the study material I use have these really ambiguous explanations of each...

In order to help with server load, we are splitting up the larger threads. This is a continuation of the original Random Thoughts thread located here https://www.physicsforums.com/showthread.php?t=338126

Hi everyone, I have the following exercise. Fx(x)=0, x<-1 or x>1 Fx(x)=1/2, x=[-1;1] g(x)=x^2+1 --- this is the function of random variable I must calculate Fy which is the sum of solutions of g(xk)=y , Fy(y)=sumFx(xk)/|g`(xk)| g(x) is bijective on [-1;1] y=x^2+1=> x=+sqrt(y-1) or x=-sqrt(y-1)...

Dear all, I don't understand why the Cosmic Microwave Background's angular distribution is considered to to a Gaussian random field initially. The rest of the analysis is roughly clear to me, COBE/WMAP/PLANCK measure the CMB Photons and show the temperature fluctuations w.r.t. the mean...

I learned that random errors cannot be controlled and cannot be eliminated but only be reduced (averaging allows a result that is below the accepted answer to be accounted for by another result that is higher than the accepted result) and so it would cause bad precision. While systematic errors...

Hi Everyone! I have two normally distributed random variables. One on the x axis, the other on the y axis, like a complex normal random variable. I'm trying to find the pdf of the angle between a fixed point on the x-y plane(let's say point 1,0) and the vector formed by combining the two...

Homework Statement Give a method for generating a random variable with distribution function F(x) = 1/2(x+x^{2}) 0<x<1 The Attempt at a Solution From what i can tell i am supposed to do something like: Let U be a uniformly distributed random variable over (0,1). U =...

The cumulative distribution function of a continuous random variable is given as follows: 0 0 ( ) 0 5 5 1 5 X if x x F x if x x           a. Determine and name the density function of . [02] b. Use both and ( ) X F x to find P(X  3) . [05] c. Find the variance of ...

Oke this is a simple question but it has me a bit stumped. Given a random variable X with a uniform probability distribution between [0,2]. What is the probability distribution function (pdf) of X^2 ?

Homework Statement Let X and Y have the joint probability density function f(x,y)=k(1-y), if 0<x<y<1 and 0 elsewhere. a)Find the value of k that makes this pdf valid. b) Find P(X<3/4,Y>1/2) c) Find the marginal density function of X and Y d) Find the expected value and variance of X and...

Homework Statement The joint PDF (probability density function) ##p_{X,Y}(x,y)## of two continuous random variables by: $$ p_{X,Y}= Axy e^{-(x^2)}e^{\frac{-y^2}{2}}u(x)u(y)$$ a) find A b) Find ##p_X (x), \ p_{y}, \ p_{X|Y}(x|y), and \ p_{Y|X}(y|x)## Homework Equations The first...

f(x)=1, θ-1/2 ≤ x ≤ θ+1/2 Given that Z=(b-a)(x-θ)+(1/2)(a+b) how would you show that Z has a continuous uniform distribution over the interval (a,b)? Any help would be much appreciated.

Homework Statement X is a normal random variable with mean 1, variance 4. 1. Find P( X(X-1) > 2 ) 2. Find a value 'a' for which P(|X| > a ) = .25 The Attempt at a Solution I had no idea how to start 1. For 2, i got this far then got stuck: P(|X| > a) = 1 - P((X-1)/2 <=...

Homework Statement Consider a random walk on a circle of N points, labeled {0,1,...,N-1}. Let the initial state be X = 0 and define T to be the first time all points have been visited at least once. Show that the distribution of X[T] (i.e. last unique position visited) is uniform over...

How does one go about dealing with a linear differential equation with random but constant coefficients (e.g. X''(t) + A*X'(t) + B*X(t) = 0 where A and B are random variables, but are constant with time)? I've searched for things like random differential equations and stochastic differential...

I have a query on a Random process derived from Markov process. I have stuck in this problem for more than 2 weeks. Let r(t) be a finite-state Markov jump process described by \begin{alignat*}{1} \lim_{dt\rightarrow 0}\frac{Pr\{r(t+dt)=j/r(t)=i\}}{dt} & =q_{ij} \end{alignat*} when i \ne...