Distribution function Definition and 133 Threads

I've been playing around with some MD simulations, a field not really familiar to me. I put together a code in LAMMPS to simulate a Lennard-Jones fluid and compute the RDF. I get the oscillations one would expect, which is good, but what is surprising is that the minimum of g(r) after the first...

Homework Statement Show that there is no minimum for the normal distribution function e^(-(x-μ)^2/(2 σ^2))/(sqrt(2 π) σ) Homework Equations The Attempt at a Solution I figured I'd take the derivative and set it equal to 0, but then what?

Hello...!I need some help...! Let the distribution function F of a random variable X given in the following attachment. Calculate the following: P(X=-1), P(X<0), P(X<=0), P(X=1), P(X>5), P(X>=5), P(3<=X<=4). I think that these are the answers:P(X<0)=F(0-)=0.1, P(X<=0)=F(0)=0.2...

Homework Statement $$P_x(x)=A(1- \frac{|x|}{2}) \ \ \ |x|≤2$$ $$P_x(x)=0 \ \ |x|>2$$ Find A Homework Equations The Attempt at a Solution This one shouldn't be too bad but I wanted to verify that I am on the right track. I basically have ##P_x(x)=A(1- \frac{x}{2})## when x≤2. 0 otherwise...

Homework Statement given pdf: f(x) = 2/3x for 0<=x<=1 f(x) = 2/3 for 1<x<=2 f(x) = 0 elsewhere Find the CDF. Homework Equations The Attempt at a Solution I've found: F(x) = 0 for x<= 0 F(x) = 1 for x>=2 F(x) = (1/3)x2 for 0<=x<=1 and I found: F(x) = (2/3)x...

Hi I have a question , the question asks find value of a and b such that F(x) is a valid cumulative distribution function? 1-a*exp(-x/b) x≥0 F(x)= a*exp(x/b) x<0 My attempt to solve the problem: I know F(x) when x goes to ∞ in 1 and when x goes to -∞ is...

Hello I was wondering If anyone could give intuitive explanations for the multivariate Gaussian distribution function and mahalanobis distance? My professor didn't explain these in probability class, they were only defined... Where did the formula come from? Why is the Gaussian function the...

The distance of someone from the center (cable station) of a circle is depicted as r, and the regular radius of that circle(the cable station) is depicted as rc. The Circle represents the entire area the cable station provides cable service for. Given: Probability Distribution Function P(r) =...

Homework Statement Let's consider a distribution function f=f(t,x^i,E,p^i). Is it true that \mathop {\lim }\limits_{p \to\infty}p^{\alpha}f=0 \forall\alpha\in R ?Homework EquationsThe Attempt at a Solution I think so, not sure though. Thanks in advance!

Hello, I'm David. I'm a new member here. Could anyone of you help me? Where can i find the formal deduction of Gauss' Normal Distribution Function? I've read a lot of statistics books and never found that. Where that comes from? It's just curiosity, not homework. P.S.: sorry about my...

Homework Statement Let N(x) denote the CDF of the standard normal density. So, it's the integral of the standard normal density from -∞ to x. Is it true that \lim_{b\to 0} N(\frac{a}{b}) = N(\frac{a}{\lim_{b\to 0}b}) = N(+\infty) = 1? 2. The attempt at a solution This is more of a...

Homework Statement Incoming signal has normal distribution, xmin is equal to -sigma, xman is equal to +sigma. What is the governing equation of the nonlinearity through which the signal has to be passed in order to make its pdf uniform? Homework Equations...

Dear all, In classical molecular dynamics simulation initial velocities are generated using the so called Maxwell distribution. At low temperature it's no longer effective, so I'm wandering whether there is a similar way to generate velocities at low temperature taking into account quantum...

Homework Statement The continuous random variable X has cumulative distribution function given by F(x) = \left\{ {\begin{array}{*{20}c} 0 & {x \le 0} \\ {\frac{{x^2 }}{k}} & {0 \le x \le 1} \\ { - \frac{{x^2 }}{6} + x - \frac{1}{2}} & {1 \le x \le 3} \\ 1 & {x \ge 3} \\...

Homework Statement (From Probability and Statistical Inference, Hogg and Tanis, Eighth Edition, 5.1-5) The p.d.f. of X is f(x) = \theta x^{\theta - 1} for 0<x<1 and 0<\theta<\infty. Let Y = -2\theta \ln X. How is Y distributed? Homework Equations Um... Fundamental Theorem of...

I just downloaded scilab because Wolfram Alpha wouldn't want to plot the function I'd like. In a physics problem I've found the temperature distribution of a 2 dimensional system. I'd like to visualize this function in 3d. The function I want to plot is u(x,y)=\frac{1}{\pi} \arctan \left (...

Okay, this is a really basic question. I'm just learning the basics of QM now. I can't wrap my head around the idea that the radial distribution function goes to zero as r-->0 but that the probability density as at a maximum as r-->zero. How can this be? they are opposite to each other...

Let X be continuous a random variable who's support is the entire real line and who's cumulative distribution function satisfies the initial value problem F'(x)=s\cdotF(x)a\cdot(1-F(x))b F(m)=1/2 note that a>0, b>0, s>0 and m is real. m is the median of the distribution, Is it...

Homework Statement A die is rolled until the first time that a six turns up. We shall see that the probability that this occurs on the nth roll is (5/6)n−1 · (1/6). Using this fact, describe the appropriate infinite sample space and distribution function for the experiment of rolling a die...

Homework Statement A continuous random variable X has density f(x) = ax2(1- x) for 0 < x < 1, and f(x) = 0 otherwise. Here a is a constant, to be determined. Find the distribution func- tion FX, the constant a, the expectation E(X), the variance Var(X), and the conditional probability p(X...

A dart is thrown towards a quadrilateral defined by {(x,y): 0 < x < b, 0 < x < b}. Assume the dart is equally likely to land anywhere within this shape. Let Z be denoted by the (x,y) coordinate with the least value. Find the region in the square corresponding to {Z < z} so i know the sample...

Homework Statement Let the independent random variables X1,X2,X3 have the same cdf F(x). Let Y be the middle value of X1,X2,X3. Determine the cdf of Y. Homework Equations F(x) = P(X<=x) = ∫-inf to x f(y)dy The Attempt at a Solution I don't understand the question, what does it...

Homework Statement ∫3/43x2e-(x/4)3 Homework Equations F(x) = 0∫xf(t) dt The Attempt at a Solution The solution is 1 - e-(x/4)3 I have tried integrating but I am not able to arrive at the solution... What is the indefinite integral of e-(x/4)3?

Hello, I am new. I been looking on the net for a guide how to solve the CDF by hand, i know the answer and I am about to crack this baby but I got stuck... Im trying to calculate Cumulative distribution function by hand: \int^{1}_{-1}\frac{1}{2\pi} e^{\frac{-z^{2}}{2}} dz or wolfram alpha...

If a random variable X follows Gamma Distribution Function with parameters K and thita, what does (X+k) follow? if K is a constant. I think, since adding the constant is just like shifting the origin, the nature of the curve remain unchanged. But what about its parameter? Thanks.

Hi, I am trying to model a PDF of frequency for the WCDMA handset. I have found some info on ways of graphing a PDF of transmit power but nothing on frequency. I am hoping there is a way to model this, but think it might be something that requires field tests with multiple phones. Any...

Hi all, I'm really banging my head on this problem: Let f be a real-valued measurable function on the measure space (X,\mathcal{M},\mu). Define \lambda_f(t)=\mu\{x:|f(x)|>t\}, t>0. Show that if \phi is a nonnegative Borel function defined on [0,infinity), then...

Homework Statement Let X and Y be two independent random variables with the same probability density funtion over: f(x) = {1/a if x € [0,a] {0 if x=0 Find the density distribution of a) X + Y and b) X*Y Homework Equations The Attempt at a Solution Ok, my...

I was wondering, does anyone have any images that show the difference between the radial distribution functions for hcp and fcc lattices? I would be useful for reference purposes.

X and Y are 2 independent gaussian random variables with parameter a. Z = XY / (X-Y) W = XY / |X-Y| I am to find the joint distribution function of z and w. I know how to find pdf of Z but how could I use it to find the joint distribution function of z and w?

Hello everybody. I have the following problem: I am given a Speed distribution function, f(v). This distribution is normalized to the total number of particles there are, that's equivalent to: \int_0^\infty f(v) dv = n_0 (particles traveling away from my target are not considered.)Now. I know...

Hi, i am running a hard disks molecular dynamics simulation. I would like to compare the radial distribution function obtained from my simulation with the theoretical radial distribution function. May i know what is the theoretical radial distribution function? Or what data do people normally...

For (4), when I calculated the Distribution Function, I had to break it up into two cases whether or not the point was above or below the line. For (6.c), I got the right answer for the Cov(X,Y), but I didn't break up the double integral into two cases. Is this because since the density...

Homework Statement Given the probability distribution function: See attachment. Determine the: 1. Probability density function. 2. The mean. 3. The median. Homework Equations Hello, I am really struggling with this subject area, this is an example I have found, would...

Hey everyone! I'm building a "Deal or No Deal" calculator that estimates the odds of getting a better deal than the one presented. As you can see in the title, I'm looking for a function that will calculate the CDF. For ease's sake, please only post JavaScript code (no C,Perl,BASIC,etc.)

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled.png?t=1298077701 Oops. Nevermind. It is in the family. I think the rest of my work is correct. http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110218_190456.jpg?t=1298077991

Homework Statement I have been given the distribution function F_X of the random variable X and I am asked to find the distribution function F_Y of Y, another random variable which is defined from X in the following way. Y={\stackrel{X^{2} if X<2;}{4 if 2\leq X < 3;}\stackrel{4(4-X) if...

i have two random variables x e y independent and they're uniform on the interval [0, 1] find cumulative distribution function of Z= (x+y)/(x-y) i just try to solve... [PLAIN]http://img202.imageshack.us/img202/5647/97250438.jpg is it right?

Homework Statement A PC generates "random" numbers from [0,1], programmed such that the distribution function F(x) of a continuous random variable X, which is satisfies the formula: F(x) = 0 , x<0 x , 0<=x<0.25 0.25 , 0.25<=x<0.5 x2, 0.5<=x<1 1 , 1<=x THe problem then asks the values of...

Hi everyone, So I am taking a statistics course and finding this concept kinda challenging. wondering if someone can help me with the following problem! Suppose X is a discrete random variable with moment generating function M(t) = 2/10 + 1/10e^t + 2/10e^(2t) + 3/10e^(3t) + 2/10e^(4t)...

Given: P(X=x, Y=y)=\frac{a^ye^{-2a}}{x!(y-x)!} where x=0,1,2,...y and y=0,1,2...\infty, and a>0 Find P(X=x) and P(Y=y) An example is provided in a book on books.google.com Page 96...

consider rolling a die. S= {1,2,3,4,5,6} P(s)=1/6 for all s in S X= number on die so that X(s)=s for all s in S Y= X^2 compute the cumulative distribution function Fy(y) = P(Y<=y), for all y in the set of real numbers. My guess for Y=1 i get...

hello, How do i find a Distribution Function based on Measurements? Y.S

Homework Statement The experiment is to toss two balls into four boxes in such a way that each ball is equally likely to fall in any box. Let X denote the number of balls in the first box. Homework Equations What is the cumulative distribution function of X? The Attempt at a...

Radial distribution function -- weird result Dear all, I think I'm having trouble with my radial distribution function (RDF) calculation and would greatly appreciate it if anyone could give me some insight. I was testing my RDF calculation subroutine to get RDF for certain colloidal...

Okay, this is a really basic question. I'm just learning the basics of QM now. I can't wrap my head around the idea that the radial distribution function goes to zero as r-->0 but that the probability density as at a maximum as r-->zero. How can this be? Thanks!

Theorem: Let F(x) be the distribution function of X. If X is any r.v. (discrete, continuous, or mixed) defined on the interval [a,∞) (or some subset of it), then E(X)= ∞ ∫ [1 - F(x)]dx + a a 1) Is this formula true for any real number a? In particular, is it true for a<0? 2) When is...

Homework Statement Given: f(x,y) = x + y, for 0<x<1 and 0<y<1 f(x,y) = 0, otherwise Derive the joint distribution function of X and Y. Homework Equations N.A. The Attempt at a Solution Using the definition, I obtained part of the joint distribution F(x,y) = (1/2)(xy)(x+y)...

Homework Statement Consider a population of individuals with a disease. Suppose that t is the number of years since the onset of the disease. The death density function, f(t) = cte^{-kt}, approximates the fraction of the sick individuals who die in the time interval [t, t+Δt] as follows...

Homework Statement For the random variable X with probability density function determine the distribution function F(x) http://img20.imageshack.us/img20/3314/questiontsy.jpg Homework Equations Cumulative Distribution Function The Attempt at a Solution Integrate f(x) to get...