Probability density Definition and 273 Threads

Statistics Jill is expecting a vist from her uncle Tom. Tom would just come whenever he felt like it, but not when he had his art class. He will either visit her in the morning, or late afternoon, between the times of 9-12am or between 3-5pm. Say X is the number of hours after 7am, what would...

Homework Statement Let f(x) = (1 + ux)/2 for -1<= x <= 1 and 0 otherwise . where -1<= u <= 1 a) show f is a density Homework Equations TO show 1. f(x) >= 0 2. intergeral f (from -infinity to infinity) = 1 The Attempt at a Solution I have done 2. and proved that it is 1...

If I have a wave function \Psi(x,x') for two identical fermions, then I have learned that the particle density at x is n(x)=2\int|\Psi(x,x')|^2dx' |\Psi(x,x')|^2 is the probability density of finding a particle at x and a particle at x'. Does this mean that \int|\Psi(x,x')|^2dx' is the...

Could anyone help me figure out the the probability density function (pdf) of |X|^(1/2)+|Y|^(1/2)+|Z|^(1/2) if X, Y and Z are distributed normally with mean 0 and variance 1, N(0,1) ? Thanks in advance.

Like the title, I don't quite understand what probability density is and its difference with probability. Can someone explain a bit on this?

Homework Statement The potential for an infinite square well is given by V=0 for 0<x<a and infinite elsewhere. Suppose a particle initially(t=0) has uniform probability density in the region a/4<x<3a/4 : a.) Sketch the probability density b.) Write an expression for the wavefunction...

I have ~5.24a_o where a_o is the Bohr radius given by 5.291772E-11 m. This is my r value. But I am getting HUGE radial probability densities ~10^8! How is this possible? I thought they have to be less than 1 since it's a probability! P(r) = |rR(r)|^2 = [r^2 / (8a_o^3)] [(2-r/a_o)^2] exp(-r/a_o)

Homework Statement Calculate the probability that the electron in the ground state of a hydrogen atom is in the region 0 < r < 3.75a0. Homework Equations a0=.0529 nm P(r)=4(Z/a0)^3*r^2*e^(-2Zr/a0) The Attempt at a Solution I am confused because I am not sure if I am supposed...

Homework Statement Probability of a car starting up is 0.9 Probability of a car NOT starting up is 0.1 Cars are tested until 2 functional cars are found. Find Bernoulli probability function associated and PROVE that it is a pdf (probability density function). Homework Equations...

I'm just curious as to how to prove that a Bernoulli distribution probability function is valid (ie. that it is indeed a probability distribution function). I have a hunch that all we do is add up all of the probabilities associated to every x value, but I'm not sure. Can someone confirm this...

Homework Statement A particle of mass m is attached to a spring with a spring constant k. The particle is moved a horizontal distance A from the equilibrium point and released from rest. We follow the motion for half a period, that is x \in [-A, A] . Show that if we take snapshots of the...

Probability density function after filtering Hello, I am trying to find how a random variable will transform once gone through a filter. For example, I have a random sequence x(t), going through a filter h(t). Thus, y(t) = x(t)*h(t) ; % '*' is convolution. Now I want to find out how...

I am tyring to solve the follwing problem... http://www.imagedump.com/index.cgi?pick=get&tp=549226 What is the appropriate K valuefor this to be a legitimate probability density function? Im not exactly sure of the approach to this problem...

Homework Statement A Particle is described by the normalized wave function psi(x,y,z) = Ae^(-alpha[x^2 + y^2 + z^2]) Where A and alpha are real positive constants a)Determine the probability of finding the particle at a distance between r and r+dr from the origin hint: use the volume of...

Homework Statement Consider the wave packet defined by psi(x) = integral(limits of +infinity and - infinity) dke^(-alpha(k-k_0)^2) e^(ikx) a)What is the mean value of the momentum p barred (it's just a line over the p) of the particle in the quantum state given by this wave function...

Sorry for not using template but you should find everything in the image provided: Hey guys. All of the info for the problem is in a picture. I've tried working on this for ours and I still can't seem to get the trig identities right :(...

Hey guys. All of the info for the problem is in a picture (sorry for not using the template). I've tried working on this for ours and I still can't seem to get the trig identities right :( http://img208.imageshack.us/img208/1770/assignmentquestion2.jpg NOTE THAT THERE SHOULD BE ANOTHER...

Homework Statement Suppose that a point (X_1 , X_2 , X_3) is chosen at random, that is, in accordance with the uniform probability function over the following set S: S = {(x_1, x_2, x_3) : 0 \leq x_i \leq 1 for i =1,2,3} Determine P[(X_1 - 1/2)^2 + (X_2 - 1/2)^2 + (X_3 - 1/2)^2) \leq...

Homework Statement Let X be a random number from (0,1). Find the probability density function of Y = 1/X. Homework Equations The Attempt at a Solution I keep thinking this is easier than I am making it out to be, but the only places I find anything similar searching is on two...

Homework Statement From Hoel, Port, & Stone, Chapter 4, Exercise 9: Construct an example of a density that has a finite moment of order r but has no higher finite moment. Hint: Consider the series \sum_{k=1}^{\infty} k^{-(r+2)} and make this into a density. Btw, this is for my own...

How to find the probability density function of a simple harmonic oscillator? I know that for one normal node is should be a parabola but what is the formula and how do we derive it?

Please help me with this. Any suggestions are greatly appreciated. Imagine that I have a bank account. X is the amount of cash on the account at time t+1. Y is the amount of cash at time t. The amount of cash depends on the deposits made and on the amount of cash during the previous period...

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...

Hi I have a question about zero point of probability density of particle. In general we say if probability density is zero at a certain position, the particle never arrive there. But I also read some post in this forum. They said zero probability density means you have zero chance of seeing the...

Suppose that h is the probability density function of a continuous random variable. Let the joint probability density function of X, Y, and Z be f(x,y,z) = h(x)h(y)h(z) , x,y,zER Prove that P(X<Y<Z)=1/6 I don't know how to do this at all. This is suppose to be review since this is a...

Assume that two random variables (X,Y) are uniformly distributed on a circle with radius a. Then the joint probability density function is f(x,y) = \frac{1}{\pi a^2}, x^2 + y^2 <= a^2 f(x,y) = 0, otherwise Find the expected value of X. E(X) = \int^{\infty}_{- \infty}\int^{\infty}_{-...

Let X, Y, and Z have the joint probability density function f(x, y, z) = kx(y^2)z, for x>0, y<1, 0<z<2 find k \int_{0}^{2}\int_{- \infty}^{1}\int_{0}^{\infty}kxy^2z dx dy dz This integral should equal 1. Is my procedure correct so far? I don't manage to solve the integral...

I am trying to calculate the variance of the position of a particle in a one dimensional box (quantum mechanics). I have a wavefunction, and I know the probablilty density is the integral of (the wavefunction squared) with respect to x. Can you please tell me how this wavefunction could be...

(\Triangular" distributions.) Let X be a continuous random variable with prob- ability density function f(x). Suppose that all we know about f is that a </= X </= b, f(a) = f(b) = 0, and that there exists a value c between a and b where f is at a maxi- mum. A natural density function to...

Homework Statement A production line is producing cans of soda where the volume of soda in each can produced can be thought of as (approximately) obeying a normal distribution with mean 500ml and standard deviation 0.5ml. What percentage of the cans will have more than 499ml in them...

HI Can anybody tell me how to calculate a PDF of y, where y is a function of x, such that y = a X*X + bX + C (i.e. a quadratic equation), and X follows the Normal Distribution X ~N(0, sigma) Help anybody? Thanks

I feel embarassed for asking, but is there a fast way to calculate this without using integration by parts? \int 2e^(-2x)x^-1dx, 0 <= x < infinity There's supposed to be some kind of trick, right?

The question is: if X is an exponential random variable with parameter \lambda = 1, compute the probability density function of the random variable Y defined by Y = \log X. I did F_Y(y) = P \{ Y \leq y \} = P \{\log X \leq y \} = P \{ X \leq e^y \} = \int_{0}^{e^y} \lambda e^{- \lambda x} dx =...

The analytical solution for the wavefunction of a hydrogenic electron with quantum numbers n, l and m has a spherical harmonic part that involves theta and phi (in spherical coordinates). I was looking in Griffiths, and the spherical harmonics part only has phi as exp(i m phi) where i is the...

[SOLVED] Probability Density Consider a gas made of single hydrogen atoms (not diatomic hydrogen gas). The ground state energy of an electrons bound to a single hydrogen atom is -13.6 eV, and the energy of the first excited state is -10.2 eV. Ignoring the spin of the electron, the degeneracy of...

Let the random variable X have the probability density function f(x). Suppose f(x) is continuous over its domain and Var[X] is bounded away from zero: 0 < c < Var[X]. Claim: f(x) is bounded over its domain. Is this claim true? I don't think a counterexample like X ~ ChiSq_1 applies...

If we have 2 different probability density functions p(x) and q(x). Then we find the expected values of function g(x) by using these 2 different probability density functions. Do both of them give the same expected value?

given that x has an exponential density function ie p(x) = exp (-x) and x(n) & x(m) are statistically independent. Now y(n) = x(n-1)+x(n) what is the pdf (probability density function) of y(n)

Hi, I need a verification for this question. Can some one help me? Question: A man enters the pendulum clock shop with large number of clocks and takes a photograph. He finds that most of the pendulums were at the turning points and only a few were captured crossing the mid point. Why is it...

[SOLVED] Klein Gordon equation, probability density Homework Statement Use the Klein-Gordon Equation to show that \partial_{\mu}j^{\mu} = 0 Homework Equations KG: \left(\frac{\partial^{2}}{\partial t^{2}} - \nabla^{2} + m^{2}\right) \phi = (\partial_{\mu}\partial^{\mu} + m^{2})...

Homework Statement Assuming that the probability density of a particle is A^2 sin^2(kx), is the particle localised in space? Using the uncertainty principle determine the degree to which the momentum of the particle is specified. A is just a constant, k is the wavenumber, x is position...

Find a constant c such that f(x,y)=cx2 + e-y, -1<x<1, y>0, is a proper probability density function. My idea: f(y) 1 =∫ f(x,y) dx -1 So I have found f(y), now I set the following integral equal to 1 in order to solve for c: ∞ ∫ f(y) dy = 1 0 Integrating, I get something like...

ok iv have been stuck on this problem for like 30 mins it says "suppose x is a continuous random variable taking values between 0 and 2 and having the probability density function below." the graph below shows a triangle with the coordinates (0,1) (2,0) then it ask what is the Probably...

Q: Given f(x) = cx + (c^2)(x^2), 0<x<1. What is c such that the above is a proper probability density function? Solution: 1 ∫ f(x) dx = 1 0 => 2(c^2) + 3c - 6 =0 => c= (-3 + sqrt57) / 4 or c= (-3 - sqrt57) / 4 => Answer: c= (-3 + sqrt57) / 4 (the second one rejected)...

[b]1. Homework Statement A vendor at a market buys mushrooms from a wholesaler for $3 a pound, and sells them for $4 a pound. The daily demand (in pounds) from custumers for the vendor;s mushrooms is a random variable X with pdf f(x) = 1/40 if 0 (greater than) x (less than) 40 and 0...

Homework Statement http://img204.imageshack.us/img204/2097/34629164kd2.jpg The Attempt at a Solution I know how to compute something like Pr(x<0.25) for example, but I'm unsure how to do it for an exact number like in question (ii). I attempted to integrate and then sub x=1/4 where...

if x is a continuous random variable from -1 to 1...how do you find c: f(x) = c + x , -1 < x < 0 c - x, 0 < x < 1 Do I integrate each one? Where do I go from there? Thanks!

Homework Statement When an electron has tunnelled through a potential barrier it's wavefunction is described by a plane wave traveling in the positive x direction. In this region the probability density is constant. I am trying to explain why it is constant but can't find any info in books or...

proposal: Gravity is an effect of uncertainty gradients. Probability density currents are recognised phenomina in quantum mechanics/dynamics. A wave-particle's uncertainty is acknowledged as a fundamental property, oscillating through space and time. The classic experimental...

J.S. Bell (Physics Vol.1, No. 3, 1964) excludes from consideration any distribution \rho of the hidden variable \lambda that formally depends on the vectors a and b , except if \rho ( \lambda ,a,b) = \rho ' ( \lambda ,a) \rho ' ( \lambda ,b) i.e. if the distribution can be factored in a...