Distribution Definition and 1000 Threads

Question is as follows: (a) = 0.4114 is the answer. Yet all I see from this answer is that X is simple equal to "0.4114". If it is "X ≤ 3" shouldn't "0.2061", "0.0692", and "0.0115" contribute to the answer somehow because they are "<" smaller than 3? I feel like I may be missing a...

Homework Statement Santa has n types of presents. Every child can receive at most one present of each type and: a) every child has to get a present AND cannot receive the same set of presents as any other child. b) for every 2 children, there must be a present that both of the children get How...

Hi, I'm doing a fit using Chi-square distribution. I have a data set and their errors, I found the best estimate minimizing Chi square, as usual, and I like to found the error bars of my best estimates but I don't know how to do that. Which is the standard form to do it?

How do I sketch the radial distribution of a $3d_{x^2-y^2}$ orbital? :D

Homework Statement A sealed container of 0.10 m3 holds a sample of 3.0x1024 atoms of helium gas in equilibrium. The distribution of speeds of the helium atoms shows a peak at 1100 m s-1. Take the mass of a helium atom to be 4.0 amu. I, calculate the temperature and pressure of the helium gas...

Homework Statement This is the problem I am given. . It is in he picture below or in the thumbnail. I was also told that since ##n## is big enough that I can use normal approximations. Homework EquationsThe Attempt at a Solution I think that ##C_{\alpha}=C_{0.1}=2.33## which I got off the...

Homework Statement A Non-Uniform but spherically symmetric charge distribution has a charge density: \rho(r)=\rho_0(1-\frac{r}{R}) for r\le R \rho(r)=0 for r > R where \rho = \frac{3Q}{\pi R^3} is a positive constant Show that the total charge contained in this charge distribution is...

Can someone explain why the probability of the inclination angle of a binary system being less than i_0 is 1-cos(i_0) i.e. why the fractional distribution of binary stars is df = sini * di, where i is the inclination angle? Where does the sin i come from? Why is not not uniformly distributed...

This is probably a stupid question , but, It's easy enough to show that the mle of a poission distribution is ## \bar{x}##: ## \hat{ \lambda}= \bar{x} ## But,I'm then looking at the generalized ratio test section of my book, multinomial, it esitmates ## \lambda ## for some data by ## \sum...

I have 2 related questions about Earth-like planets and solar systems: First question: - I don’t understand why the Earth has so much iron. - How much iron is blown off by the typical supernova in proportion to other metals? - If the proto-solarsystem was a rotating gaseous disk, should most...

Hi, For my math methods 3 course, I am not quite sure which books to use. The course is based on the math methods book by Riley, Hobson, and Bence, and I don't particularly like it. Hence, I am looking for some alternatives. Especially for the Preliminaries section. I had a real hard time...

Homework Statement A molecule has a velocity v and speed v. I've worked out (and understand) that the number of molecules in a gas with speeds between v and v+dv and moving at angles between Ө and Ө+dӨ to any chosen axis is: (1/2)nf(v)dvsin(Ө)dӨ The internet verifies this. f(v) is the speed...

Hi there, how one can compute the spectral power distribution of white LED ,i,e like black body radiator that has a formula of calculation.. regards

Hello, I was wondering if H_{ii} (that is the ith diagonal element of a random matrix) has the same distribution with its corresponding eigenvalue, say \lambda_{i}. Thanks

Homework Statement Using the Boltzmann distribution for a small system in contact with a heat reservoir at temperature T, find the Maxwell-Boltzmann distribution. Homework Equations The Boltzmann distribution states that the probability density of a system in contact with a heat reservoir at...

If the electric field and boundary conditions are known exactly for a region of space, is it true that there exists only one charge distribution in that region of space that could have produced it? My understanding of the uniqueness theorem in electrostatics is that for a given charge...

derivation of wiens displacement law and wiens distribution law from thermodynamic principle.but not from Plancks law

Homework Statement http://web.phys.ntnu.no/~kolausen/TFY4230/.oldExams/17_eksdes12.en.pdf solution: http://web.phys.ntnu.no/~kolausen/TFY4230/.oldExams/18_losdes12.en.pdf Look at problem 4a, formula (27) or the expression between (29) and (30). My professor keeps converting sums into...

Hopefully this has not already been asked. It would be hard to do a forum search with the right words to find it if it has been already. I am wondering if it is ever possible or common place to generate power in a Wye generation scheme and then connect it directly to a transformer with a...

Homework Statement Can I measure the probability of a person being at a certain end location after n steps using the binomial distribution if, probability student goes x=x+3 is 0 <= p <0.5 , x=x-1 is 0<= 0.5 p <1.Homework Equations x=x+3 is 0 <= p <0.5 x=x-1 is 0<= 0.5 p <1 The Attempt at a...

when considering the quantum harmonic oscillator, you get that the wave function takes the form psi=ae^{-\frac{m\omega}{2\hbar}x^2} I have been trying to integrate \psi ^2 to find the constant a so that the wave function is normalised, and I know the trick with converting to polar coordinates...

My son "invented" a simple board game. It consists of a series of squares numbered 1 to 32. You start at square 1, then advance your piece according to the throw of a die, until square 32 is reached, and you win. Nothing else happens, and the only difficulty is that square 32 must be reached...

Homework Statement Z = X - Y and I'm trying to find the PDF of Z. Homework Equations Convolution The Attempt at a Solution Started by finding the CDF: Fz(z) = P(Z ≤ z) P(X - Y ≤ z) So I drew a picture So then should Fz(z) be: since, from my graph, it looks as though Y can go from...

Hello everyone! New member here, as an ME major I always seem to come across very valuable information here, so I figured I would see if possibly someone here could help me. The problem I am dealing with involves modeling a car through certain motions such as hitting a speed bump, and part...

Hello, I would like to ask the following question : --> I have an object of mass M (represented by the blue potato in the two attached drawings). --> I know the coordinates (x,y) of its Center of Gravity (reprensented by big red cross). --> I also know the coordinates of its contact points to...

Hi everybody, i have a problem that i wanted to share with you if we consider a polycrystal made of cylindrical fibers following a von mises-fisher distribution equation (17) in http://bit.do/vmisesfisher (called orientation distribution function of fibers) . i must change the probability...

I’m working on a chemistry problem, which essentially translates to finding the answer to a related probability problem. However, my knowledge in probability is very limited and I'd be grateful if someone could help me out with it. The following is the problem:- Suppose I have a bag containing...

I am looking for more information (e.g., reference, the CDF and descriptive stats) about a four-parameter skewed generalized Gaussian (SGG) distribution. I have come across the PDF for this distribution, but with no reference and not a lot of other information. Here is a snippet... On...

Considering a unit mass of an ideal gas in a cylindrical container of volume 'V' at temperature 'T' the pressure exerted by the gas at the walls of the container is given by the ideal gas equation as, pV=RT where 'R' is the characteristic gas constant for the particular gas. Under equilibrium...

I have a quick(?) question about log-normal distribution. As far as I know, the right-side equation (from wiki) is the PDF of log-normal distribution. However... How I can get the left-side equation...?? I do not know how I can get the normalized log-normal function? please help me...

When two states |k> and |k'> degenerate, a perturbation H' would lead to an energy split of <k|H'|k'>. As the number of degenrate states increases, the order of the secular equation rises correspondingly (and the equation could hardly be solved ?) My question is: is there any knowledge of the...

I have a question considering the transformer's short-circuit test and the impedance (or short-circuit voltage). The transformer's general data is: Rated power: 50kVA Primary voltage: 10000V (10kV) Secondary voltage: 420V (0,42kV) Primary current: 2.89A Secondary current: 68.73A Vector group...

The probability density function of the lifetime of a certain type of electronic device (measured in hours), X, is given by  f(x) = 10/x^2, 0, x > 10; elsewhere. (a) Find the cumulative distribution function of X, namely F(x) and hence find P(X > 20). (b) What is the...

Hey guys, I'm trying to find a conditional distribution based on the following information: ##Y|u Poisson(u \lambda)##, where ##u~Gamma( \phi)## and ##Y~NegBinomial(\frac{\lambda \phi}{1+ \lambda \phi}, \phi^{-1})## I want to find the conditional distribution ##u|Y## Here's what I've got so...

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?