Distribution Definition and 1000 Threads

Suppose X and Y are independent Poisson random variables with respective parameters λ and 2λ. Find E[Y − X|X + Y = 10]3: I had my Applied Probability Midterm today and this question was on it. The class is only 14 people and no one I talked to did it correctly. The prof sent out an e-mail saying...

I have a question regarding electric potential and infinity. So, "A square of side length a with uniformly distributed positive charge lies on the yz plane with its center at the origin. What does the graph of the potential along the x-axis look like? The answer given in the textbook is a...

Homework Statement Suppose that A, B, C are independent random variables, each being uniformly distributed over (0, 1). ) What is the probability that all the roots of the equation Ax2 + Bx + C = 0 are real? Homework Equations (b) What is the probability that all the roots of the equation...

Homework Statement You purchase a chainsaw, and can buy one of two types of batteries to power it, namely Duxcell and Infinitycell. Batteries of each type have lifetimes before recharge that can be assumed independent and Normally distributed. The mean and standard deviation of the lifetimes...

Hello, I have two jobs,Normal distribution with mean of 4.5 minutes and standard deviation of 1.5 minutes for type 1 and uniformly distributed between 1 and 3 minutes for type 2

Hey everybody, I'm an engineering Ph.D. so my knowledge of n-dimensional Euclidean spaces is lacking to say the least. I'm wondering what sort of approach I can take to solve this problem. ##\boldsymbol{1.}## and ##\boldsymbol{ 2. }## I am given a probability distribution for a random...

Homework Statement Use the Maxwell-Boltzmann distribution of speeds to find the fraction of F2 molecules at 500 K which have speeds in the range 240 to 250 m s -1 (HINT: determine the fraction of the total area under the distribution curve represented by the part between these two speeds...

Homework Statement A cylinder contains an ideal gas and rotates at angular speed w. Find the probability that a molecule is at radial position r from the axis of the cylinder. Homework Equations Boltzmann distribution, P(E)∝Ω(E)exp(-E/kT) where Ω(E) describes the degeneracy of the energy level...

Homework Statement All charges in space are distributed on the xy-plane. The potential above the plane is known as \phi = \phi_0 exp(-kz) cos(kx) What's the charge distribution on xy-plane? Homework Equations \vec E =- grad(\phi) The Attempt at a Solution Applying the relationship between...

Let X be random variable and X~N(u,σ^2) Thus, normal distribution of x is f(x) = (1/σ*sqrt(2π))(e^(-(x-u)^2)/(2σ^2))) If we want to standardize x, we let z=(x-u)/σ Then the normal distribution of z becomes z(x) = (1/σ*sqrt(2π))(e^(-(x^2)/(2)) and we usually write Z~N(0,1) But as you can see...

Homework Statement Problem(s): Suppose that X has an exponential distribution with mean equal to 10. Determine the following: (a) P(X > 10) (b) P(X > 20) (c) P(X < 30) (d) Find the value of x such that P(X < x) = 0.95. Correct answers: (a) 0.3679 (b) 0.1353 (c) 0.9502 (d) 29.96 Homework...

Homework Statement i want to measure temperature distribution of a heated cylinder. it become my final project, and now, i feel confuse, how to measure it. i think on put LM 35 DZ on every point at the cylinder, heat the cylinder, and read the output. but that should take a lot of cost...

Homework Statement Suppose X has the Uniform (0,1) distribution. Find the median of the distribution of e^X correct to 2 decimals. Homework Equations F(X) = 0.5 F(X) = ∫f(x) The Attempt at a Solution I am not entirely sure what to do here, I know to find the median you need to find when F(X)...

Homework Statement Consider a sample of size 5 from a uniform random distribution (0,1) . Computer the probability that the median is in the interval (1/4, 3/4). [/B]Homework Equations I guess... The Pdf of beta is and median is...I'm not sure...I would guess 1/2?[/B]The Attempt at a...

I've been trying out induction cooking on a small one-burner unit, with a large cast iron pan. I'm getting the expected hot spot in the center of the pan, and a serious temperature falloff toward the sides. No surprise there - the induction element is about 7" (I dismantled the unit to check)...

In the figure given the capacitance for the two pair would be same. Can anybody please explain me how the charge would be distributed across each plate? I think that the middle plate being isolated should have +Q on one side and -Q on other, but how would be the charge distribution about the...

Homework Statement For the next probability function: f(x)=x/4 for 0<x<2 Homework Equations a) Get the probability function b) Get the cumulative distribution function The Attempt at a Solution I don´t know if the problem is well written, and for that I'm lost with the first question...

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...

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...