Distribution Definition and 1000 Threads

Homework Statement If X is uniformly distributed over (0,1), find the PDF of Y = |X| and Z = e^X Focusing on the |X| one Homework Equations Derivative of CDF is the PDF The Attempt at a Solution So I start by writing down the CDF of X, Fx(x): 0 for x <0 x for 0 ≤ x ≤ 1 1 for x ≥ 1 And I...

Homework Statement Question Homework Equations Equation The Attempt at a Solution Attempt I am not sure how to write the |r-r'| in a way that allows me to actually solve the integral. I have tried writing |r-r'| in spherical co ords, but all I seem to be able to get is this as the separation...

Homework Statement $$f:\mathbb{R} \rightarrow \mathbb{R},$$ $$ f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-(x-\mu)^2}{2 \sigma ^{2}}}$$ What are the roots of this equation? Homework EquationsThe Attempt at a Solution The roots of an equation are the values of x such that f(x) = 0. This...

Homework Statement Let x be an exponential random variable with lamda = .5 P(x=5|2<x<9} = 0 since exponential is continuous => probability of any single number = 0 Calculate E[x| 2<x<9] = integral from 2 to 9 of (x* .5*exp(-.5*x)) dx ? is this true or is there something wrong because of the...

I am sure this has a simple answer, but I don't seem to get it at the moment. I am going through a derivation of the Boltzmann's distribution by maximising the entropy with the constraints that the sum of the probabilities add to 1 and the average energy is some constant value. My question is...

Homework Statement If ##X_1,..,X_n## is a random sample and has a density ##f_X(x)=6x(1-x)## for ##0<x<1##. Let ##X_{(1)}=\min(X_1,..,X_n)##. Find the ##E(X_{(1)})## (Expected Value)? Homework Equations There is an uploaded picture of the pdf I used. The Attempt at a Solution "I've been...

I'm working on a project studying sea ice in the Arctic ocean. A brief overview of the essentials: The ice pack over the Arctic begins shrinking every summer beginning around June 1st, and begins to recover around Sep 15th. I'm interested in the movement of the ice edge as the pack shrinks...

Homework Statement I have to determine the radius at which 50% of energy is in a Gaussian profile.Homework Equations The intensity is given by I=Ioe^(-r/2c)^2. This is just a gaussian function ofcourse. The Attempt at a Solution I know c is the standard deviation. I searched through charts...

I am facing problems while comparing the results of solving a problem individually using both the concept of Binomial Distribution of Probabilities and the Classical Definition of Probability. Let me formulate the problem first: "The probability that a pen manufactured by a company will be...

Homework Statement a man draws balls from an infinitely large box containing either white and black balls , assume statistical independence. the man draws 1 ball each time and stops once he has at least 1 ball of each color . if the probability of drawing a white ball is p , and and q=1-p is...

The loggamma distribution is defined by $$ g(x) = \frac{1}{ \Gamma ( α) θ^{ α} } \frac{(ln( x))^{ α - 1}}{x^{1+\frac{1}{θ}}} $$, for $$ 1 < x < ∞ $$ where α is a positive integer. I've been trying to find the mean and variance of this distribution. It's been somewhat frustrating because the...

Homework Statement 2. Homework Equations [/B] So the sample mean is 2. the sample variance would be [[(3-1+1)-1]/12]/36 = 8/432. The Attempt at a Solution Is it, P[ (2.1-2)/sqrt(8/432) < z < (2.5-2)/sqrt(8/432)] = 0.232574. The book answer is 0.2312. I just want to be sure.

Given a one-dimensional Gaussian distribution, distributed as following: f (x) = exp (-x ^ 2 / (2q)) / q / √ (2pi) proof which q is the standard deviation Thanks !The standard deviation is defined by: http://www.mathsisfun.com/data/standard-deviation-formulas.html

Homework Statement A rectangular chip of dimensions a by b is insulated on all sides and at t=o temperature u=0. The chip produces heat at a constant rate h. Find an expression for u(x,y,t) Homework Equations δu/δt = h + D(δ2u/δx2 + δ2u/δy2) x∈(0,a), y∈(0,b) The Attempt at a Solution I'm...

I would like to ask what does mean energy distribution ,and how can I calculate the energy distribution of transmitted electrons . Thanks

Do charges exist as a point or a distribution? Or does it depend on the situation? Or does the concept of image mean that it's very difficult to tell, and if so why is the point charge model being pushed so hard, what phenomena does it explain that distributions cant?

In statistical mechanics the boson distribution function has the well known form ##f = \frac{1}{e^{E/T} - 1},## (in the special case of zero chemical potential). As one considers the non-equilibrium variant this generalize to ##f = \frac{1}{e^{\frac{E}{T(1+ \Theta)}} - 1},## for some function...

Homework Statement Using Darcy’s law, plus another appropriate relationship, derive a single equation for the pressure distribution in a porous material. Your equation should be stated in terms of generic operators (i.e. without assuming any specific coordinate system) and allow for the fact...

I have an asymetric probability distribution function (pdf), in this case we know that the concept of an error bar does not seem appropriate. Well I'm finding the shortest interval that enclosed the 68% of probability. My problem is that my pdf couldn't be integrated analytically and I'm using...

Homework Statement A spherical charge distribution is given by p = p_0 (1- \frac{r^2}{a^2}), r\leq a and p = 0, r \gt a , where a is the radius of the sphere. Find the electric field intensity inside the charge distribution. Well I thought I found the answer until I looked at the back of...

A mode of frequency ##\nu## has energy ##E_n = h \nu##. In terms of photons, the interpretation that I have read several places, is that this correspond to ##n## photons of energy ##h \nu##. Furthermore, it is stated that the probabilty of finding ##n## photons at frequency ##\nu## is given by...

Homework Statement Hi all - I have been trying to evaluate part II of this problem for a long time now... For a simplified model of a proton's charge distribution, Find the constant of proportionality required to normalise ρ correctly. Show that Homework Equations N/A The Attempt at a...

Homework Statement Two test charges are located in the x–y plane. If q1 = -3.50 nC and is located at x = 0.00 m, y = 0.680 m and the second test charge has magnitude of q2 = 3.60 nC and is located at x = 1.00 m, y = 0.650 m, calculate the x and y components, Ex and Ey, of the electric field, ...

Background: I am trying to write a program for Buckingham Pi Groups. I need to find a way to list all the input varialbes as different sets. For example if I have 4 variables [V D p u] and I want to distribute them 3 ways I get 4 sets. Number of Sets = Binomial(Number of Variables...

Homework Statement You throw a coin a 100 times, what's the probability of getting 50 tails? Homework Equations The Attempt at a Solution We have n=100 , p=1/2, q=1/2 and k=50 we substitute in the first equation we get: P= 100!/ (50! * 50!) * (1/2)^100 The factorials are not simple to...

I'm going over the Physics GRE and this question has me a little confused. The configuration of the potassium atom in its ground state is 1s2 2s2 2p6 3s2 3p6 4s1. The answer to which of the following is true is this statement: "Its electron charge distribution is spherically symmetrical." Is...

So, the exercise is to find the expected value of following distribution: f(x) = 0,02x 0<x<10 answer in the book says 6,67 As far as I knowe, the expected value is calculated by the Integral of x * f(x) between 0 and 10, in this case! It looks like this won't give the result 6,67! what am...

If \(Y = -X\) and \(X\sim Ber(1/4)\), then what is Y? I know that \[ X\sim \begin{cases} 1 - p, & x = 0\\ p, & x = 1 \end{cases} \] where \(p = 0.25\) in this case. What is the negative of \(X\) though. It doesn't make any sense making the probabilities negative.

Homework Statement i need to show that the peak of the maxwell Boltzmann distribution is equal to 1/2 kt. Homework Equations maxwell Boltzmann distribution according to modern physics 3rd edition by kenneth kramer. ill try to do my best with this N(E)= \frac{2N}{√∏}...

In carrom game, we have black/white small disc pieces, just imagine we have a single piece of it on the board.We hit that pieces with a striker on one side of the four wall. And the pieces goes on hitting side of the wall, number of times. If I'm right, there cannot be a general formula...

Homework Statement Here is the question, which itself is rather confusing. A nonuniform surface charge lies in the yz plane. At the origin, the surface charge den- sity is 3.5 μC/m^2. Other charged objects are present as well. Just to the right of the origin, the electric field has only an x...

Hi to you all! I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, that slides over that string. For the given parameters p,k and n one must must...

The derivation of the maxwell Boltzmann distribution involves maximizing the number of ways to obtain a particular macrostate with respect to how the particles are distributed in their respective energy states. One then arrives at $$\frac{n_i}{n} = \frac{1}{Z} e^{- \beta \epsilon_i},$$ where...

Hello all, How would I do this question by hand? I know I integrate from -infinity to +infinity for $f_x,y$, but I have no idea how to do it by hand! My algebra soup is bad, can someone please help me? P.S I heard some of my friends talking about some 'trick' you can do with the exponential...

What exactly prevents us from ruling out a uniform distribution on infinite sets? To be more precise, why are distributions and limits like \int_{-\infty}^{+\infty}dx\,\lim_{\sigma\to\infty}f_{\mu,\sigma}(x) = 1 \int_{-\infty}^{+\infty}dx\,\lim_{\Lambda\to\infty}\frac{1}{\Lambda} \chi_{[a,a+L]}...

How does the texture of a surface affect the concentration of charge on that surface? Say we compare a balloon (smooth) and a football (textured) (ignoring material differences) and give them the same total charge. Then we introduce dust particles. How do the two surfaces attract dust...

1. A harried passenger will miss by several minutes the scheduled 10 A.M. departure time of his fight to New York. Nevertheless, he might still make the flight, since boarding is always allowed until 10:10 A.M., and extended boarding is sometimes permitted as long as 20 minutes after that time...

The lecturer did not explain this for some reason. Assuming that we have a gass where all the particles have a certain absolute velocity v. Directions of v vector are random though, giving velocity vector a uniform direction distribution. That means that a velocity vector of any random...

Gammaray bursts (GRB) may affect the prevalence of life in various different regions of the galaxy. http://arxiv.org/abs/1409.2506 On the role of GRBs on life extinction in the Universe Tsvi Piran, Raul Jimenez (Submitted on 8 Sep 2014) As a copious source of gamma-rays, a nearby Galactic...

I accidentally posted this to the "Calculus & Beyond" forum when I meant to post it to the physics forum. If someone can tell me how to move this post, I will get rid of it here! Homework Statement Consider a property, for example temperature θ, that is conserved during advection (i.e. Dθ/Dt =...

Homework Statement A solid conducting sphere of radius 2.00 cm has a charge 16.00 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a total charge of -3.00 µC. (Take radially outward as the positive direction.) Find...

I've noticed that the vast majority of named or important mathematical constants, are what you might call small numbers. Their modulus lies very often in the range [0,5]. Here's two examples of tables: http://en.wikipedia.org/wiki/Mathematical_constant#Table_of_selected_mathematical_constants...

Residential DC power distribution, well that’s the end goal. The main question is about stepping down a 24v 4amp lead acid deep cycle battery bank to accommodate normal DC usage voltage. For example 24v 4amp too: 12v 1a, 5v 400ma, 9v .4a, 12v 2a. Was thinking of making adjustable outlets so...

I'm trying to interpret the expression of a microcanonical distribution for energy E_0 of a particle of mass m moving about a fixed centre to which it is attracted by a Coulomb potential, Zr^{-1}, where Z is negative. The function expression looks like this: ρ_{E_0}(\textbf{r,p}) = \delta(E_0...

what is the best software to calculate power losses in a distribution system?

Hi, I have never quite worked this type of probability question out, so would like some help please. Imagine this scenario: There are 4 people sat around a table, A, B, C and D. A is sitting opposite C, B is sitting opposite D. There is a bag with 16 balls numbered 1-16. The balls are...

The following problem is from "Probability and Statistics in Engineering - Hines, Montgomery" A potential customer enters an automobile dealership every hour. The probability of a salesperson concluding a transaction is 0.10. She is determined to keep working until she has sold three cars...

Hi, I understand that Volume of Distribution (Vd) = elimination constant (k) * Clearance (Cl), but I can't visualize why clearance would be proportional to volume of distribution. Can someone help explain this to me? I feel like it should be a more complicated relationship. Clearance = Mass...

Homework Statement i am having problem with part iv ) . the ans is 0.04519 . can anyone tell me how to do this ? i have solved part i , ii and iii ..p/s line 1: [SIZE="3"][SIZE="2"]A tank contain 10^5 cm3 of water Homework Equations The Attempt at a Solution

Hi, I'm struggling to know what distribution this question requires, and what should be signalling the distribution type: A manufacturer claims at most 5% of his product will sustain fewer than 1000hrs of operation before needing service. Twenty products are selected at random from the...