Distribution Definition and 1000 Threads

Homework Statement The random variable ##(x,y)## has density ##f(x,y) = ce^{-(ax+by)}## for ##0\leq y\leq x\leq 1##, with given constants ##a > 0##, ##b > 0##. 1. Compute the constant ##c##. 2. Find the conditional probability density ##f_y(y|x)##. 3. Compute the regression curve of ##Y## on...

I've calculated the joint distribution, XY_PDF(x,y) of random variables X and Y (both coming from a distribution N(n) = C*e^(-K*n^2)). I use XY_PDF(x,y) to calculate the joint distribution AR_PDF(a,r) of the random variables A (angle) and R (radius), with the PDF method and the Jacobian. Since...

I'm looking to measure the weight of an tennis racket at different lengths. Obviously If I stick it on the scale it will give roughly the sam,e weight no matter if I put the whole racket on, or a third of the racket. Would there be a way I could measure the weight, of say the first third of an...

Okay, my online class has posed another word problem and I cannot seem to understand this week's material or how to formulate a solution. Here it is: Imagine you are in a game show, a money give-away! There are 4 prizes hidden on a game board with 16 spaces. One prize is worth \$4000...

hi, so my lecturer decides to give me manic depression by sending me on a wild goose chase. what is the general form of a plot of Ψ, Ψr2 and r2Ψ versus r for both Ψ2s and Ψ2p orbital... am not even sure i said it right So far I have only gotten the Ψ2r2 versus r

hi, so my lecturer decides to give me manic depression by sending me on a wild goose chase. what is the general form of a plot of Ψ, Ψr2 and r2Ψ versus r for both Ψ2s and Ψ2p orbital... am not even sure i said it right

i have a question, why is the plot of r2(Ψ2p)2 not a good representation of the probability of finding an electron at a distance r from the nucleus in a 2p orbital

Homework Statement A student sits a test and is told that the marks follow a normal distribution with mean 100. The student receives a mark of 124 and is told that he is at the 68th percentile. Calculate the variance of the distribution. Homework Equations...

I modeled a simple cantilever rectangular beam in Patran of (L,W,H = 100, 6, 4) with Hexa8 elements and applied a vertical shear load (upwards) of some magnitude at the free end. Ran in Nastran and plotted the vertical shear stress distribution on a cross-section in middle of length (in order...

Homework Statement Using direct integration, compute the electric field at the point (0,0,Z) of a semi-espherical (z > 0) charge distribution of radius R < Z and density ##\rho=constant## having a spherical hole of radius ##r_h<R## centered at (0,0,##r_h##). Homework Equations Coulomb's law...

I Have a Dumb Question. If Electricity Supplied from Substation to Feeder to Transformer and Under Transformer If There Are Many Consumers. Assuming That many Consumers Went on for a Holiday, Does Utility Still Pay for the Electricity to the Generation company for the Electricity they Supplied...

Homework Statement The Weibull distribution is used frequently as a lifetime distribution and is so is used a lot in survival analysis. It can be parameterised as:##f(x;\lambda,k) = \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-\left(\frac{x}{\lambda}\right)^k}## for ##x\geq 0## &...

Hi all, I am analysing the flow of water in a subsea pipe, and have been getting stuck in trying to solve the energy equation to plot a temperature distribution across the pipe diameter I have derived the equation as such seen in my attachement. But my main question is how should/would I...

Homework Statement Show the steps needed to obtain the equation for average molecular speed, cavg=√8RT/πM from the integral (from negative infinity to infinity) ∫v*f(v)dv where f(v) is the Maxwell distribution of speeds function f(v)=4π*(M/2πRT)1.5v2e-Mv2/2RT M is the molar mass of the...

This is a question about transforming a probability distribution, using the blackbody spectrum as an example. Homework Statement An opaque, non-reflective body in thermal equilibrium emits blackbody radiation. The spectrum of this radiation is governed by B(f) = af3 / (ebf−1) , where a and b...

What is electric field distribution around two conductor cable connected to DC power supply? Assume power supply is isolated and not grounded. Assume cable is straight. Case 1: no current runs through the cable. One wire is positive, another – negative. Negative or zero? If we think in terms of...

I'm battled by my thought of interception. The entangled photon between Alice and Bob, suppose the one at Alice's side is already measured to be 1, so the second is heading over to Bob to be 0. Eve gets to it first and measures it to be 0. Knowing its 0, eve prepares a photon of state 0 and...

I've written a program that simulates placing pieces randomly on an nxn chessboard, one by one until 2 are adjacent. When 2 are adjacent I stop, and I report the number of pieces it took. I've plotted a histogram of the number of pieces it took vs number of occurences just to see what kind of...

Hello, For this type of question: There are 5 green and 45 red marbles in the urn. Standing next to the urn, you close your eyes and draw 10 marbles without replacement. What is the probability that exactly 4 of the 10 are green? I understand that I can use Hypergeometric distribution, which...

Homework Statement 1. According to the Maxwell-Boltzman law of theoretical physics, the probability density of a gas molecule is ##f(v) = kv^2e^{-\beta v^2}## if ##v > 0## and ##f(v) = 0## otherwise, where ##\beta## depends on its mass and absolute temperature, and ##k## is an appropriate...

Homework Statement A multiple choice test consists of a series of questions, each with four possible answers. How many questions are needed in order to be 99% confident that a student who guesses blindly at each question scores no more than 35% on the test? Homework Equations So I know that...

Hi all, I refer to the following pdf document, in particular the appendix: http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974A%26A...37..183A&link_type=ARTICLE&db_key=AST&high= End goal is to distribute N stars each having mass m (looks like equal mass stars is the easiest scenario)...

Homework Statement A gas has a hypothetical speed distribution for N gas molecules with N(v) = Cv^2 for 0 < v < V0. Find (i) an expression for C in terms of N and v0 (ii) the average speed of the particles Homework Equations N/A The Attempt at a Solution (i) integrating N(v) with respect to v...

Homework Statement \textbf{The Logarithmic Series Distribution}. We will examine the properties of a the Logarithmic Series Distribution. We will check that is is a probability function and compute a general term for factorial moments and, hence, compute its mean and variance. This distribution...

Homework Statement Homework Equations The Attempt at a Solution Im confused by this question, just looking at the diagram without any maths you can see what would happen. C and D would want to reach equilibrium and be at the same level so the pressure down on D would be the difference in...

Hi, what are the possible reasons for selecting 11kV underground distribution system vs 22kV underground distribution system for urban area. I know about 22kV can carry twice the load compared to 22kV. How about impacts of pricing, fault level, stepdown from 132 kv to 22/kv etc. Thanks

Homework Statement [/B] A company produces batches of 1800 axle shafts . These are tested to determine the proportion of those with too rough surface according to the standards set in the industry. The quality control department of a sample of 150 axle shafts in a lot and concluded that there...

Hi all, I saw some figures about potential (contour) plot in some articles that has some beautiful gradient lines. The shape is quite weird but you can see clearly there are some strong concentration of potential at some places. For example, if you have 300x300 grids, there shows strong...

Hi, i'm performing a simulation about this potential http://motion.cs.umn.edu/PowerLaw/ I calculated the radial distribution function succesfully but i don't know how these guys are normalized the other pair distribution function, as a function of time to collision. Could anyone help me? Thanks!

Hi, I'm writing a mathematical expression of energy distribution of a signal, and in the formula I’ve found first and second derivative of delta function. I have to analyze my result but couldn’t found how to read these two derivative from an energy point of view. And how can we see further...

Hi!, If we have a bidimensional system of N particles. How can i parametrize a radial distribution function g(r) in another single variable ? This variable is the "time to collision", which we define as the duration of time for which two particles could continue at their current velocities...

Homework Statement I'm trying to find the combined per unit reactance of this distribution system shown. Homework EquationsThe Attempt at a Solution I've calculated all the individual per unit reactances but I'm having trouble combining them. It's a very simple problem, but I just want to make...

I'm watching a Stat. Mech. lecture and in it, the lecturer mentions a "general probability distribution" but doesn't explain what exactly that is, yet in the context of the video, everything necessary to understand is understood. On some cursory google searches I'm finding several hits for a...

Homework Statement We ask a person to taste 18 biscuits , 8 made to butter ( the other 10 are made to margarine ) , and to identify 8 butter cookies . He does not know the exact number of butter cookies . As he sees no difference , he randomly selects those he claims to be butter . Y = the...

Homework Statement A charge distribution has uniform density in the x-y directions and varies with z according to: ρ(z) = ρ0e−|z|/t where ρ0 and t are constants. (a) Find the potential V (z) and the electric field E(z) (b) Sketch them clearly showing their behaviors in the regions |z| ≪ t...

1. Does anyone know why for an isotropic distribution function, pressure tensor reduces to a scalar pressure? For instance, for a Maxwellian distribution P=A ∫ vx vy exp-(vx2 + vy2 + vz2) dvx dvy dvz is not zero. I think everybody should realize how bogus some of the authors are. Google...

Homework Statement Consider f = wT x, where p(w) ∼ N (w|0, Σ). Show that p(f|x) is Gaussian. The Attempt at a Solution [/B] So there are apparently two approaches to this problem using either the linearity of f in terms of w or moment generating functions. But I'm having a lot of trouble...

Homework Statement For my project I need to compute the average the number of photons given by the expression: ##\bar{n}= \frac{e^{-\bar{h}\omega/\kappa T}}{1-e^{-\bar{h} \omega / \kappa T}}## where ##\kappa## is the Boltzmann constant and ##\omega## is the oscillator frequency. For the...

Let's say my probability function is given by: p(y1,y2)=Γ(y1+y2+γ)/((y1+y2)!*Γ(γ)), when γ>0 is known. I suppose it is from an exponential family but I can't write in canonical form because I'm only familiar with exponential family with one variable so I'm confused now when there's to variable...

Homework Statement A three-phase distribution transformer is configured as follows: -primary side = star with solidly grounded neutral -secondary side = delta, grounded via zigzag earthing transformer A single phase-earth fault occurs on the secondary (delta) side of the circuit...

Homework Statement a) ∫δ( x² cos x) dx with x from -∞ to +∞ b) Integral over C, with C = unit circle ∫C δ(α-α0) a ds a =(1,1) Homework Equations a) δ(g(x)) =∑δ(x-xi)/|g'(xi)| b)? The Attempt at a Solution a) g(x) = x² cosx g'(x) = 2x cos x - x² sin x xi = 0 and (2n+1)π/2...

Hi Guys :) I have become interested in producing true random numbers of uniform distribution, and have come across this Numberphile video in my travels: The narration hints at the topic of converting numeric sequences of a curved distribution, inherently more likely to be closer to a mean...

Homework Statement Homework Equations ıt is nonhomog type ,2D heat conduction problem The Attempt at a Solution I don't understant To parts so I couldn't attemp a solution.

Please bare with me, this is my first post here (although I've read a lot on here over the past few months) Hopefully I've used the correct formatting etc. I've got to a sticking point on the final point of the question below (2iii) I'm pretty happy with my answers to 2i and 2ii so I've not...

Coulombs law states 2 point charges of opposite sign will attract where acting simultaneously on two point charges and as follows: The formula calculates the force that will act and implies the force be equally experienced by both points of charge even if one charge is much greater than...

Hello everyone, I'm stuck at a elementary stochastic problem. I have to calculate means, variance and co-variance for two random variables. Homework Statement Let r,g,b∈ℕ. r red, g green and b black balls are placed in an urn. The balls are then drawn one at a time with replacement, until a...

Homework Statement Hello, we were given homework, which is perfectly described by this picture. We should figure out F1 and F2 (it's number). I know that if the both angles are equal, it is easy to solve. However, now i should solve a situation when first angle (alpha) = 50 grades, the second...

Hello, Just looking into some clarrification. If a customer states that they want the following system, what is it they mean (note, it is 3-phase 4W 120/208V: 1200 A MAIN DISTRIBUTION C/W: 1- 600 A house panel feed 2 - 100 A tenant sections 2 - 200 A tenant sections Basically the 1200 A is...

Hello. I have a problem calculating the electric field from spherical charge distribution. The exercise is: 1. Homework Statement Homework Equations To solve the problem for $$ 0\le R < a$$ i tried 2 ways: $$ \vec{E} = \frac{\vec{a_R}}{4\pi\epsilon_0}\int_v\frac{1} {R^2}\rho dv $$ and the...

Hello all I have this question I am trying to solve. In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement. X - the minimal number we see Y - the maximal number we see I need to joint distribution. I understand that X is getting the values 1,2,3 while...