Random Definition and 1000 Threads

Homework Statement Random vector Y = [Y_1 Y_2 Y_3 …. Y_m]' where ' = transpose mean = u and and ∑ = covariance Z = N_1 * Y_1 + N_2 * Y_2 + …. + N_m*Y_m all N are numbers Find the covariance of Z E[ (Y- E[Y] )(Y - E[Y] ) ] = E[YY'] -E[Y]E[Y]'= [N_1 N_2 .. N_m] [∑ - u^2 ….∑ -u^2] ' This...

Hi, Suppose we're looking at a random sequence of digits from 0 to 9. We start off reading the digits until every digit from 0 to 9 has been seen at least once and we mark the count of digits read up to that point (run length). We then reset the run length and continue until the whole random...

I have a mean mu, and an exponential distribution function. How do I use a random number, generated with a PRNG, to get a random number from the distribution? I know this is a really basic question. Please help :) Thanks

Hi, i was wondering if the following is valid: E[x/y] = E[x] / E[y], given that {x,y} are non-negative and independent random variables and E[.] stands for the expectation operator. Thanks

Homework Statement X is uniform [e,f] and Y is uniform [g,h] find the pdf of Z=X+Y Homework Equations f_z (t) = f_x (x) f_y (t-x) ie convolution The Attempt at a Solution Obviously the lower pound is e+g and the upper bound is f+h so it is a triangle from e+g to f+h...

Homework Statement A drunk lurches from one lamp post to the next on his way home. At each lamp post he pauses and is equally likely move towards or away from home. Suppose the posts are separated by a distance ##a## and find the mean and standard deviation of his displacement ##d## from the...

The lowest value for {the expected number flips of a fair coin to get a random (uniform) digit} seems to be 4.6. Can you prove this? Can this be beat with a biased coin?

Does skin vibrate at the molecular level? If so does it have a steady frequency? If so would it be possible to use a laser to detect said vibration from a distance?

How does a random number generator work ? What is the usage of it ?

Hello, i m trying to evaluate the following: r*x - r*y ≤ g, where r,x,y are nonnegative random variables of different distribution families and g is a constant nonnegative value. Then, Pr[r*x - r*y ≤ g] = Pr[r*x ≤ g + r*y] = ∫ Fr x(g + r*y)*fr*y(y) dy, where F(.) and f(.) denote CDF and...

If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution? I tried to do this with the sum of bernouli variables and...

Hello I am trying to solve this problem: A coin is given with probability 1/3 for head (H) and 2/3 for tail (T). The coin is being drawn N times, where N is a Poisson random variable with E(N)=1. The drawing of the coin and N are independent. Let X be the number of heads (H) in the N draws...

Homework Statement A couple is expecting the arrival of a new boy. They are deciding on a name from the list S = { Steve, Stanley, Joseph, Elija }. Let X(ω) = first letter in name. Find Pr(X = S). Homework Equations The Attempt at a Solution Ok the answer is 2/3. How is it 2/3...

using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ConsoleApplication1 { class Program { public class RandomNextDemo { static void NoBoundsRandoms(int seed) { Console.WriteLine(...

This is part b) of an assignment question. In part a) we were asked to derive the Fokker Planck relation for the biased random walk. The answer is: dP/dt = -vdP/dx + D d2P/dx2 Where the first term is the drift term due to the biased motion and the second term is the diffusion term. Then...

Have you read a book called "A Million Random Digits with 100,000 Normal Deviates"? Once you’ve read it from start to finish, you can go back and read it in a different order, and it will make just as much sense as your original read! This is just one of the reviews for the book on amazon.com...

Hi, http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf (see page 8, sum of two independent random variables). I don't understand why they had to go further into the limits, 1 < z < 2. Why do they have to do that? And also, where did they get it...

Hello, I am working on the two point correlation function in dark matter haloes. Right now i need to create an array of rundom numbers to compute the estimators. My question is: How can i create a random distribution of points in the unit sphere (having in mind its curvature). I...

Homework Statement Word for word of the problem: Let N (t, a) = At be a random process and A is the uniform continuous distribution (0, 3). (i) Sketch N(t, 1) and N(t, 2) as sample functions of t. (ii) Find the PDF of N(2, a) = 2A. Homework Equations A pdf is 1/3 for x in...

I don't completely understand why the area of the proof circled in red is true. Any advice would be appreciated. https://dl.dropboxusercontent.com/u/33103477/Q1.jpg

Homework Statement There are a set number of marbles in a bag; the marbles consist of two colors. We are given the mean number of marbles of color 1 in the bag, as well as color 1's standard deviation. We are then asked to find the mean and standard deviation of color 2.Homework Equations How...

Assume X is a random variable under a probability space in which the sample space ?= {a,b,c,d,e}. Then if I am told that: X({a}) = 1 X({b}) = 2 X({c}) = 3 X({d}) = 4 X({e}) = 5 And that: P({a}) = P({c}) = P({e}) = 1/10 P({b}) = P({d}) = 7/20 Find the C.D.F of X, the density of X...

Can you please help me find the density of the following functions? The density of an absolutely continuous random variable X is: fX(x) = { (3x^2-1)/12 if 1<x<2 { 1/2 if 2<x<3 { 0 elsewhere Find the density of Y where Y = 4X-2 Find the density of M where M = (X-2)^2 Thank you!

Let x \in \{-1, 1\}^n and let p(x) = \{w \in \mathbb{R}^n : x \cdot w > 1\}. What is the probability that p(x_1) \cap \ldots \cap p(x_{n+1}) = \emptyset given that x_i are chosen uniformly at random?

Find cov(Y,Z) where Y = 2X_1 - 3X_2 + 4X_3 and Z = X_1 + 2X_2 - X_3 Information given E(X_1) =4 E(X_2) = 9 E(X_3) = 5 E(Y) = -7 E(Z) = 26 I tried expanding cov(Y,Z) = E(YZ) - E(Y)E(Z) but can't figure out how to calculate E(YZ)

Hi, I have a quick question. Let R and S be two independent exponentially distributed random variables with rates λ and μ. How would I compute P{S < t < S + R}? I am a little bit confused because of the variables on either side of the inequalities. I have tried conditioning on both S and R...

Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean value 15.0 kips and standard deviation 1.25 kips. Compute the following probabilities by standardizing and then using Table A.3. a) P(X ≤ 15) b) P(X ≤ 17.5) c) P(X ≥...

(I wasn't sure how to title this, it's just that the statement resembles Chebychev's but with two RV's.) Homework Statement Let \sigma_1^1 = \sigma_2^2 = \sigma^2 be the common variance of X_1 and X_2 and let [roh] (can't find the encoding for roh) be the correlation coefficient of X_1 and X_2...

Homework Statement Let X_1, X_2, X_3 be iid with common pdf f(x)=exp(-x), 0<x<infinity, 0 elsewhere. Evaluate P(X_1<X_2 | X_1<2X_2)Homework Equations f(X|Y) = f(x,y)/f(y) The Attempt at a Solution Since P(X_1<X_2) is a subset of P(X_1<2X_2), the intersection (edited, at first said union)...

Hi, I am struggling trying to find the (equation of the) pdf of the sum of (what I believe to be) two non-central chi-squared random variables. The formula given on wikipedia (http://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution) shows that the random variable associated with...

Homework Statement Two RVs X1 and X2 are continuous and have joint pdf f_{X_1,X_2}(x_1, x_2) = \begin{cases} x_1+x_2 &\mbox{for } 0 < x_1 < 1; 0 < x_2 < 1 \\ 0 & \mbox{ } \text{otherwise}. \end{cases} Find the pdf of Y = X_1X_2.Homework Equations I'm using the transformation "shortcut' that...

Homework Statement Let us choose at random a point from the interval (0,1) and let the random variable X_1 be equal to the number which corresponds to that point. Then choose a point at random from the interval (0,x_1), where x_1 is the experimental value of X_1; and let the random variable...

Homework Statement Homework Equations Y=1/2*(X1-X3)^2+1/14*(X2+2X4-3X5)^2The Attempt at a Solution For (a) part, I have only learned to find the moment-generating function of Y, but not finding the p.d.f. Moreover, the examples I have seen only involves random variables Xi to the power 1, but...

Homework Statement Let X_1, X_2 have the joint pdf h(x_1, x_2) = 8x_1x_2, 0<x_1<x_2<1 , zero elsewhere. Find the joint pdf of Y_1=X_1/X_2 and Y_2=X_2. Homework Equations p_Y(y_1,y_2)=p_X[w_1(y_1,y_2),w_2(y_1,y_2)] where w_i is the inverse of y_1=u_1(x_1,x_2) The Attempt at a Solution We can...

Hi, Wasn't sure if I should post this to Linear Algebra or here. My question is really simple: Can a 2N by 2N random, and Hermitian Matrix ( Hamiltonian ) be always written as: H = A \otimes I_{2\times 2} + B \otimes \sigma_x + C \otimes \sigma_y + D \otimes \sigma_z where A,B,C,D are all...

Homework Statement Three yearly losses. First: Exponential Second & Third: Weibull Losses are independent. Find the 95% VaR of the min loss Homework Equations The Attempt at a Solution My first thought was: Let L be total loss, A be first Loss, B be second loss, C be third...

i have a simple enough question Find the MGF of a continuous random variable with the PDF: f(x) = 2x, 0<x<1 I understand MGF is calculated as: $$M(S) = \int_{-\infty}^{+\infty} e^{Sx} f(x)dx$$ which would give me $$\int_{-\infty}^{+\infty} e^{Sx} 2xdx$$ but how would i compute this...

Suppose I take a random walk on a 2 dimensional square lattice, but this lattice plane has a finite size, e.g. Dx*Dy. I can not cross the boundary, my step length is the lattice cell size, I either go straight or make turns with right angle. Is there any work on this type of random walk? If...

Dear PH, Recently I have been trying to determine if a surface is iridescence or not. The most quantitative method to achieve this is to find the maximum reflective peak, this is also highly repeatable and worked well. The idea is to move a sample at all angles of possible viewing geometry...

Hello, Homework Statement Suppose we have two boxes, numbered 1 and 2. Box 1 contains 10 white and 6 numbered red balls, while Box 2 contains 8 white and 12 numbered red balls. We take out 2 balls from Box 1 and are transferred in Box 2. Then, we choose 1 ball from Box 2. a) Find the...

Hi, I'm having a bit of a problem with a probability question. The question is Let X be a normal random variable with mean \mu and variance \sigma^{2}. Find E[(X -\mu)^{k}] for all k = 1,2,... I'm not really sure what to do and need some help to confirm how to approach the question...

How to build a random number generator circuit? Any good links / tutorials ? Thanks Ybqts

There is a chapter in Feynman Lectures on Physics called The Random Walk(41-4). I understand everything till the paragraph right after equation 41.18. I have no idea what he is trying to say. There is an equation 41.19, which is diff. eq. for object that is forced and is in a environment that...

This is not a homework question but I project I am working on and need someone with more mathematical prowess than myself. I am using a computer program to draw random numbers from two independent distributions, x1 and x2, for two different cases and I want to establish a theoretical...

Hi there, I have recently come across some data that is supposed to be random, but I don't think it is. I graphed it out and it sure doesn't look random. I also ran a couple of statistical tests such as the runs test, and they all say "not random." Visually, the data looks like a piece of...

We selected X point from interval (-1,2). If X=x, we selected point Y from (-1,x^2). Define the function of density of the random variable Y.

Given a length preserving bijection on n-bits uniformly at random, what is the expected number of cycles? Cycles being f(f(...f(x)...)) = x

Hi all, I have an all time doubt here. We know that if r.v z = x + y where x and y are 2 random sequences having corresponding pdfs p(x) and p(y), the pdf of z, p(z) = convolution ( p(x),p(y) ). I have seen the derivation for the continuous case although not thorough how to prove it. I...

I need to generate initial conditions for modeling galactic spiral arms. I start with the following polar equation: rho = a. / (log (b * tanh (theta / (2 * n))) with a, b ​​and n are parameters to choose from. to give a thickness along the curve for the generated points, I did the...

Homework Statement We are given the following table and need to find the E(XY) X|Y y = 17 20 23 35 48 p(x) x = -20 0.02 0.03 0.07 0.02 0.06 0.2 0 0 0.05 0 0.05 0.1 0.2 1 0.05 0.03 0.02 0.07 0.03 0.2 3 0.01 0.02 0.03 0 0.04 0.1 17 0.18 0.04 0.06 0.01 0.01 0.3 p(y) 0.26 0.17 0.18 0.15...