Random Definition and 1000 Threads

I am trying to derive the distribution for the sum of two random vectors, such that: \begin{align} X &= L_1 \cos \Theta_1 + L_2 \cos \Theta_2 \\ Y &= L_1 \sin \Theta_1 + L_2 \sin \Theta_2 \end{align} With: \begin{align} L_1 &\sim \mathcal{U}(0,m_1) \\ L_2 &\sim...

Homework Statement Let X and Y be rv's with joint pdf f(x,y) = 6(1-y) for 0≤x≤y≤1 and 0 elsewhere find Pr(X≤3/4, Y≤1/2) Homework Equations The Attempt at a Solution Ok I am having trouble with finding the right limits of integration for dependent variables. If we let the...

Homework Statement I want to find the PDF for arccos and arcsin of a uniform random number. Given: Y\sim\mathcal{U}(0,2\pi) \\ X = cos(Y) The Attempt at a Solution I started with trying to find the CDF: \begin{align} F_X& = P(X \le x) \\ & = P(cos(Y) \le x) \\ & = P(Y \le arccos(x))...

In order to help with server load, we are splitting up the larger threads. This is a continuation of Random Thoughts Part 2 thread located here https://www.physicsforums.com/showthread.php?t=687099&page=186

Homework Statement |zi - 3| = Pi Homework Equations Well, it clearly has to do with a circle but I do not believe there is a general equation for what I am asking about. The Attempt at a Solution There is no general solution not trying to solve anything. I want to know exactly...

Homework Statement Let ##Y_1,...Y_n## be independent standard normal random variables. What is the distribution of ##\displaystyle\sum_{i=1}^n{Y_i}^2## ? Let ##W_n=\displaystyle\frac{1}{n}\sum_{i=1}^n {Y_i}^2##. Does ##W_n\xrightarrow{p}c## for some constant ##c##? If so, what is the...

How to transform a random variable CDF to a standard normal Given F(x) = 1- exp (-sqrt x), for x greater that 0 Thanks.

Given $X$ as a negative binomial random variable with parameters $r$ and $p$. Find $E(\frac{r-1}{X-1})$. As $E(g(X))$ is defined as $\sum_{x\in X(\Omega)}g(x)p(x)$, this is my attempt in which I am stuck. What can I do next? In the case $y=r-1$, is the sum invalid? Thanks in advance!

Homework Statement I am attempting to calculate a heat transfer across a medium with known material properties. I have the equation and all but one variable I have an exact answer for. I require the variance of my answer. Homework Equations I know ALL variables (ie numerical value) except...

Homework Statement Let X and Y be random losses with joint density function f(x,y) = e^-(x + y) for x > 0 and y > 0 and 0 elsewhere An insurance policy is written to reimburse X + Y: Calculate the probability that the reimbursement is less than 1. Homework Equations Have not...

Hello All! A recent problem has stuck with me, and I was hoping you could help me resolve it. Consider the following premise: Let us assume that X \sim \mathcal{U}(-3,3) (U is the continuous, uniform distribution). And let the transformation Y be applied thus: Y = \left\{ \begin{align*} X+1...

Code: Random number less than specifed value This isn't really a homework problem. I'm just doing this for fun and giggles. But given the nature of the forum rules, I'll post it here. Homework Statement Create a method (function) that returns a random number less than the specified...

Homework Statement If the probability density function(p.d.f.) of a random variable X is f(x) = 1/6 * e-|x|/3 where x is lying in (-∞,∞) and |-x| = x if x≥0, then what is the p.d.f. of the random variable Z = XY = X*|X| where Y = |X| ? Homework Equations Nothing special. The Attempt at a...

Hi everyone, sorry to bother you with a really random question, and I hope I'm posting this in the right board, but here goes anyway... The universe is currently too small in size to write out an entire googolplex. The visible universe is 4 x 1080 m3 (according to the ever reliable Wikipedia...

Let $\Omega=\{\omega_1,\omega_2,\omega_3\}$ an sample space, $P(\omega_1)=P(\omega_2)=P(\omega_3)=\dfrac{1}{3},$ and define $X,Y$ and $Z$ random variables, such that $X(\omega_1)=1, X(\omega_2)=2, X(\omega_3)=3$ $Y(\omega_1)=2, Y(\omega_2)=3, Y(\omega_3)=1$ $Z(\omega_1)=3, Z(\omega_2)=1...

Hello, I have two random variables X and Y that can take values of the kind (a,b) where a,b\in \{ 0,1,2,3 \}. Thus, the sample space has only 16 elements. I have, say, N observations for both X and Y, and I would like to know if there is some correlation between X and Y. - How is this...

Hey! I've been doing some research on random walks. From what I have gathered, a random walker in 1-D will have: <x> = N l (2 p - 1) σ = 2 l sqrt[N p (1 - p) ] Here, N is the number of steps, p is the probability to take a step to the right and l is the step size. I was wondering what <x^2>...

Homework Statement I have a physical system, which I know the time average statistics. Its probability of being in state 1 is P1, state 2:P2 and state 3:P3. I want to simulate the time behavior of the system.Homework Equations N/AThe Attempt at a Solution I assume the rate of transition event...

Homework Statement What is the expected value of ||Ax+n|| where || || is the L2 norm and x and n are uncorrelated and E[n] = 0 The Attempt at a Solution E[ norm of Y] = E[(Ax+n)' (Ax+n)] = E[(x'A'+n')(Ax+n)] = E[x'A'xA +x'T'n +n'Ax +n'n] the three last terms = 0 due to...

Homework Statement Find the conditional distribution function and density for the random variable X defined on R given that X is in some interval I = (a,b) where P(X in I) > 0. Assume that the density and distribution for the random variable X is known Homework Equations fX|X\inI =...

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 A and B agree to meet at a certain place between 1 PM and 2 PM. Suppose they arrive at the meeting place independently and randomly during the hour. find the distribution of the length of time that A waits for B. (If B arrives before A, define A's waiting time as...

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)...