Distribution function Definition and 133 Threads

I have a question that is puzzling me as always...The Fermi-Dirac distribution function is (at T=0): f\epsilon=\frac{1}{e^{\beta(\epsilon-\epsilon_{F})}+1} and we know that we can subsitute f\epsilon by 1 for \epsilon< \epsilon_{F} and 0 otherwise. However what is f(-\epsilon)? The answer is...

Homework Statement A gas of electrons is contrained to lie on a two-dimensional surface. I.e. they have no movement in the z direction but may move freely in the x and y. a) From the equipartition theorem what is the expected average kinetic energy as a function of T? b) For T = 293K...

I have a fairly complicated pdf for Brownian motion with drift for first passage time and would like to calculate the mean and percentiles of the pdf. Is there a straightforward way of going about this? I can plot the distribution.

I've computed a distribution function f(m,v) by taking partials of P(X<m, Y<v) with respect to m, v. Suppose I wanted the distribution function for P(X-Y > a). Since I know f(m,v), can I use that to help me compute my new distribution function by taking partials? If so, how? I'm a little...

Let X be a continuous random variable with density function f(x)= .5e^|x| for x range R. Find EX and Var(x) help please!

Homework Statement The location of an emergency is uniformly distributed over a city district. The district is a square rotated 45 degrees with "radius" r (the distance from the center to the top corner is r). When the emergency occurs, the ambulance is at the center of the district. Let D be...

Homework Statement Let X have an Exp(1/2) distribution. Determine the distribution function of 1/2X. What kind of distribution does 1/2X have? The Attempt at a Solution I can't seem to do this quite properly. I thought of doing the integral from x to -inf of 1/2X dx but that doesn't...

Homework Statement I have been given a CDF of T value probabilites for t >= 0 I have been given P(t=3)=0.59 P(t=5)=0.85 Homework Equations The Attempt at a Solution I have been asked to find P(T > 5 | T>3 ) I was wondering how to work this out. As this is a conditional...

Homework Statement Let X and Y be continuous random variables having joint probability density function f(x,y) = e^{-y} if 0 \leq x \leq y A) Determine the joint cumulative distribution function F(x,y) of X and Y. (Hint: Consider the three cases 1) x \leq 0 or y \leq 0 2) 0 < x < y...

Hello! I'm taking a mathematics course in probability and stochastic processes and we started covering the CDF (cumulative distribution function) which i understand perfectly and then the PDF (probability density function). The PDF was defined to be the derivative of the CDF. Now, the CDF is...

Homework Statement The speed distribution function of a group N particles is given by: dNv=k*dv if U>v>0 dNv=0 if v>U 1) find k in terms of N and U. 2) draw a graph of distribution function 3) compute the average and rms speed in terms of U. 4) compute the most probable...

X is continuously distributed with probability density f_{X}(x) = nx^{n-1}, if 0 < x \leq 1 and f_{X}(x) = 0, otherwise Find the distribution function F(x) of X. Find the probability that X lies between 0.25 and 0.75 when n=1 and when n=2. Find the median of X, i.e. the value of a so...

Hi I have a function \phi =arctan(Y/X) where, X\sim \mathcal{N}(A\cos \theta, v) and Y\sim \mathcal{N}(A\sin \theta,v). I want to find pdf (probability distribution) of \phi . Any suggestions ? I think change of variables in integral might work??

Hey all, I have two questions. 1) The density of electron energy states is given by g(E) = A sqrt E. Evaluate how many quantum states there are with energies between 9.0eV and 9.1eV. Ansewr in terms of the quantity A. 2) Consider an intrinisic semiconductor. Let Nv and Nc be the number...

my question is regarding 'continuous' cumulative distribution functions. i kind of get it apart from that darn 't' in the definition (see http://upload.wikimedia.org/math/f/2/4/f24252ffb5e5e747b246189b7e1cfcce.png). My textbook, my lecture notes and even wikipedia don't refrer to the 't'...

Hey guys I'd like a steer in the right direction with this problem. I would like to show that P\{x_1\leq X \leq x_2\}=F_{X}(x_2)-F_{X}(x_1^{-})\quad(1) Where: X is a random variable. F_{X}(x) \equiv P\{X \leq x \} is its cumulative distribution function...

Hi guys, I have a problem understanding the derivation of the energy distribution function; i.e. the number of particles dN with energy dE, here is what I have (from literature); dN/dE = dN/dt * dt/dV * dV/dE so you can define some of these whole derivitives in terms of acceleration...

Homework Statement I have the following question p(x) = log_10(1 + 1/x) for x = 1,2,3, ... 9 (otherwise p(x)=0) So firstly I had to prove that p(x) is a probability function, which I have done so (by proving the sum of all the values =1) anyway the second thing I have to do is...

[SOLVED] Probability distribution function proof Homework Statement Prove the function p(x) = \frac{3}{4b^{3}}(b^{2}-x^{2}) for -b \leq x \leq +b is a valid probability distribution function. Homework Equations I'm not sure if it's as simple as this, but I've been using \int p(x) dx...

Homework Statement The probability density function of X is f(x) = 2x, 0 < x < 1 Find the distribution function of X. The Attempt at a Solution I just don't know what to do here. The book does something with Y and the change of variables and I don't understand why they were...

Hello, I'm familiar with the common calculus approach with partial derivatives to evaluate error propagation in calculations with random variables. However, I'm looking for a way to derive the classic formula with the sum of fractional errors squared: {\left(\frac{\Delta Z}{Z}\right)}^2 =...

Hi. Does anyone know if it is possible to start from the thermal density matrix \hat \rho_T = \frac{e^{-\hat H_0/kT}}{\mathrm{Tr}e^{-\hat H_0/kT}} and from that derive that the single particle density matrix can be written as \rho(p ; p') = \delta_{p,p'} f(\epsilon_p) just by...

Homework Statement The random variable x takes on the values 1, 2, or 3 with probabilities (1 + 3k)/3, (1 + 2k)/3, and (0.5 + 5k)/3, respectively. Homework Equations i. Find the appropriate value of k. ii. Find the mean. iii. Find the cumulative distribution function. The...

I'm reading Basdevant/Dalibard on 'Stationary States of the Hydrogen Atom' in preparation for a final this week, and the "Probability distribution function" for finding an electron in a spherical shell of thickness dr in the ground state is given. It's not derived, so I was wondering if anyone...

1.Given f(-1) = 0.15, f(1) = 0.29, f(3) = 0.21, and f(5) = 0.35, find P(X ≤ 1) 2.Given f(-1) = 0.15, f(1) = 0.29, f(3) = 0.21, and f(5) = 0.35, find F(1) 3.Given f(-1) = 0.15, f(1) = 0.29, f(3) = 0.21, and f(5) = 0.35, find P(-1 < X ≤ 3) and the rest using this distribution function...

Once again, I'm having a disagreement with my TA regarding a problem set he gave us. Here is the exact question, as written: Find the distribution function associated with the following density functions: a) f(x) = 3(1-x^2) , x an element of (0,1) b) g(x) = x^{-2} , x an element of positive...

I've gotten a weird answer after doing the problem but I'm stuck as to where I messed up. The density function is this: f_{X} (x) = \frac{1}{6}x for 0<x\leq2 = \frac{1}{3}(2x-3) for 2<x<3 and 0 otherwise And the question is to find the distribution function. So integrating for the...

Is there a way to derive P (X=r) =^nC_r p^r q^{n-r} , r= 0, 1, 2,..., n where X: B(n,p) where n is the total number of bernoulli experiments, p the probability of success q, the probability of failure.

Hi, I have the following problem to solve: Consider a planet of radius R and mass M. The plante's atmosphere is an ideal gas of N particles of mass m at temperature T. Find the equilibrium distribution function of the gas accounting for the gas itself and the gravitationnal potential of...

Could someone help me. I don't able to explain if is FG is a distribution fuction: Show that if F and G are distribution functions and 0 \leq \lambda \leq 1 then \lambda.F + (1 - \lambda).G is a distribution function. Is the product F.G a distribution function?

Could someone help me to find the probability distribution de Y below: A random variable X has distribution function F. What's the distribution function of Y = a.X + b, where a and b are constants?

This is what I have: Let the distribution function of X be given by f(x) = 0, if x < (or equal to) 5 f(x) = x/10 - 1/2, if 5<x<(or equal to) 15 f(x) = 1, if x>15 Find p(6<x<12) Ok, everyone. I need major help. I have no clue where to even begin. I have searched the web for help...

I've been practicing on how to get the probability distribution/density functions of certain random variables by solving some questions in my book. I cam across this particular problem, and though, It seems easy, the answer does not comply with what I got (or simply I got the wrong answer.)...