Distribution Definition and 1000 Threads

Homework Statement 1. Consider selecting at random a student who is among the 15,000 registered for the current semester at a school Let X be the number of courses for which the selected student is registered and suppose that X has probability distribution x: 1 2 3 4 5 6...

Homework Statement A company is interested in evaluating its current inspection procedure on large shipments of identical items. The procedure is to take a sample of 5 items and pass the shipment if no more than 1 item is found to be defective. It is known that items are defective at a 10%...

I am confused about the basic idea of probability distribution in ensembles. Given macroscopic properties of the system, a system can have large number of micro states. But isn't the probability of finding a system in any of the micro state is equal? What is then the interpretation of this...

Homework Statement The amount of time that a surveillance camera will run without having to be reset is a random variable having the exponential distribution with beta = 50 days. find the probabilities that such a camera will a) have to be reset in less than 20 days b) not have to be reset in...

Homework Statement I have run into a situation that my gut tells me is impossible (alright extremely unlikely) when assuming a Poisson distribution. I want to make this gut feeling more formal by testing it against a Poisson distribution. Sadly I'm not a schooled statistician. Generalised...

In the graphs that I see around the internet I see that the energy axis starts at 0 eV and it goes up. So the electrons have positive energies. But in the electronic band structure, the electrons have negative energies. And if they go to infinity, then their energy becomes 0. So, what is...

Homework Statement An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year. a). How many loads can be expected to occur during a 4-year period? b). What is the probability...

"A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes. a.What is the probability the calls lasted...

I am multiplying a lognormal distribution by an function to scale it larger. While I know that scaling a lognormal distribution by a constant multiplier yields a lognormal distribution, in this case the multiplier is not a constant. Instead, smaller values from the lognormal distribution are...

Using the Maxwell-Boltzmann equation above, there is an example in my book (Giancoli 4th edition p. 481) where they use this to find the average velocity. I understand that it would just be the sum of all the speeds of the molecules divided by the number of molecules. But then I'm having...

Hi there, kinda new here so please let me know if this question has been answered. I am hoping to get a link or two to some good sources of information on Lorentz transforms and distribution functions (as used in physics). I understand DF's in class and I understand the math behind them I just...

Is there a relationship between QM probability and normal distribution ? I'm thinking about drawing probability densities as functions of phase. Thanks

Homework Statement Homework EquationsThe Attempt at a Solution I believe the entire charge Q has to be given to any of the sphere such that one charge is neutral ,while the other has charge Q . In this way there would be no electric force between the two spheres and only attractive force...

In Megger testing distribution transformers, how much importance is there in including the LV/HV bushings in the test. If you disconnect and have high readings independant of the bushing, and then put the bushings back into the circuit and the readings fall dramatically, what is that saying...

Homework Statement Consider the Gaussian Distribution ## p(x) = Ae^{-\lambda(x-a)^{2}} ##, where ## A ##, ##a##, and ##\lambda## are constants. (Look up any integrals you need.) (a) Determine ##A## (I only need help with this (a)) Homework Equations ##\int_{-\infty}^{\infty} p(x)dx = 1##...

It's pretty easy to find the "working principle" of surface capacitive touchscreen like http://www.elotouch.com/Technologies/SurfaceCapacitive/howitworks.asp Roughly speaking, I know that A surface capacitive touchscreen has a conductive layer to which some electrodes are attached The...

1. The lognormal distribution is identified as a model for concentration of a certain organic matter above a certain stretch of a highway. The parameters of this distribution are sigma = 1.9 and sigma = 0.9. a) Determine the expected value and the standard deviation of such distribution. b) The...

Hi all, I study binding of analytes in a platform where I have 10.000 sensors. Theres is one binding event per sensor and I identify it as a sudden positive change in the signal. I do first a control experiment without analytes. I measure the maximum change in the signal for each sensor and I...

Hello I am an electrical engineer freshly out of school and i was wondering if anyone could help me reach an answer to this design problem. I am attempting this problem solely for personal knowledge because in school I never took a course on distribution design. I found this problem looking...

Why wavefunction (the square of its modulus) of an electron is not seen as a measure of substance/charge distribution of the electron?

The lengths of a certain species of worm follow a normal distribution. Thirty percent of the worms are at least 16cm long, and 15% of the worms are less than 10cm long. Find, to 2 decimal places, the standard deviation of the lengths of the worms.

In http://www.americanscientist.org/issues/pub/the-spectrum-of-riemannium/5, the author mentions that the function P(x) = 1-(sin(πx)/(πx))2 seems to be, assuming the Riemann Hypothesis is true, to the two-point correlations of the zeros of the Riemann zeta function. Going by...

With X having the exponential $(\lambda)$ distribution and $Y = X^3$, how do I compute the joint cumulative distribution function? Here is how far I've come: $F(x,y) = P(X ≤ x, Y ≤ y) = P(X ≤ x, x^3 ≤ y) = P(X ≤ x, X ≤ y^{1/3}) = P(X ≤ min(x, y^{1/3})$, $f_x(x) = \lambda e^{-\lambda x}$$ for...

How are protons in an ion source distributed in momentum space? Consider an ion source fed with H2 at low pressure. As soon as the protons are free protons they are accelerated by the extraction voltage of perhaps 10 kV. In momentum space the protons are initially a "shell" with a certain...

This paper: http://arxiv.org/abs/1509.02832, The Age Distribution of Potential Intelligent Life in the Milky Way, estimates the age distribution of intelligent civilazations in the Milky Way. Unsurprisingly we rank somewhat below the advancement level of termites compared to your typical ET. It...

Homework Statement A charge distribution has the form ##\rho=-\frac{q}{4\pi ra^{2}}(1-\frac{r^{2}}{a^{2}})\exp(-\frac{r^{2}}{2a^{2}})##. Compute the total charge Q, the electric field E, the potential ##\Phi##, and the electrostatic energy W for this charge distribution. Homework Equations...

Homework Statement An experimenter measures the counting rate from a radioactive source as 10,150 counts in 100 minutes. Without changing any of the conditions, the experimenter counts for one minute. There is a probability of about 15 percent that the number of counts recorded will be fewer...

Homework Statement Let X be a continuous random variable with cumulative distribution function given by F(x) = P(X<x). Define a new random variable U=F(X). Homework EquationsThe Attempt at a Solution OK so to solve this problem I first say U=F(X). F(u)=P(F(X)<u) which means F(u)=P(U<u) is...

Homework Statement The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1366. protons per square meter per second. Assuming that the depth of Earth’s atmosphere...

How is the expected frequency column worked out for each interval of trains? 2) My attempt Take the first interval, 60 - 62, I thought about doing this: (62 - mean) / standard deviation (62 - 67.45) / 2.92 = - 1.866 using Z score < - 1.886, from the normal distribution table, I get: 1 -...

hello every one , I want to know how we get phonon frequency spectrum theoretically by using three modes and dispersion relation, can anyone explain it. for example it is phonon energy correspond to density of state how it is obtain?

We know that If object is homogenius and small (like gold atom) we can use this equation to calculate total energy of object when it moves very slow due to speed of light.And the equation is ##1/2(m_1v^2+m_2v^2+m_3v^2...=1/2Mv^2##, ##(M=m_1+m_2+m_3...)## here v is small and we are talking about...

In one double slit experiment, one physicist placed a convex lens before the back screen detector. The individual photons passed through the double slit then through the lens. The individual photons then go through the focal point, then a good distance after they reach the focal point they hit...

Hi, I have a quick question. If both X and Y are uniformly distributed on the unit interval [0, 1]. Can we prove that the joint distribution of (X, Y) is uniform on the unit square [0, 1]×[0, 1]? Do we need any condition to ensure the result, such as Independence between X and Y? Thanks.

Never mind. I got this one. Couldn't figure out how to delete the post though.

Hi could someone check my answer to the question below. Question: My Answer: I_{fA} = 3I_{1A} = 3I_{2A} = 3I_{0A} \Rightarrow I_{fA} = \frac{3E}{Z_1 + Z_2 + Z_0} = \frac{33kV}{20+20+30} = 471.43A Then using the same method I got I_{fB} = 942.86A

Homework Statement Can we consider the universe to have a uniformly charged distribution? If so, shouldn't the field at any point in space be zero? Since the universe is infinite, will it be symmetrical about any point, field should be zero right? Why is this not true?[/B]2. The attempt at a...

Homework Statement An infinitely long cylinder of radius R is placed above an infinite grounded plane. The centre of the cylinder is a distance (d) above the plane, and the cylinder has a surface charge density of σ. (a) Initially ignoring the grounded plane, what is the electric field due to...

Homework Statement A ring of radius R has a current density ##\vec J=J(r, \theta) \sin \phi \hat \phi## where phi is the azimuthal angle in spherical coordinates. Calculate the charge distribution considering that it was initially null. Homework Equations Not sure. Maybe ##\nabla \cdot \vec J...

Hello, I've read in a paper that the following binomial distribution \sum_{k=floor(N/2)+1}^N{N\choose k}\varepsilon^k(1-\varepsilon)^{N-k} can be upper bounded using Chernoff bound by e^{ floor(N/2)}\,\Phi(s_0) where \Phi(s)=\left(1-\varepsilon(1-e^s)\right)^N and...

Hi all, in following the many available derivations of the Boltzmann distribution I was trying to do it by maximizing W, which is N choose n1,n2,...nt., instead of lnW, because it should give the same answer (since W is monotonically increasing with lnW, am I wrong?). So given the two...

This technically isn't a coursework or homework problem: I have a uniform Joint density function for the lifetimes of two components, let's call them T1 and T2. They have a uniform joint density function, both are positive it follows, and the region is 0<t1<t2<L and L is some positive constant...

I want to know spatial distribution (concentration) of hydrogen and phosphorus in silicon oxide film with thickness of 1 micrometer. What is the simplest possible way to obtain such distributions with adequate resolution (~50 nm)?

Homework Statement This is not really a homework problem, it's a problem that I am working on and am not able to come to an end of it. The story is: I have a certain amount of force, let's call it ##F_0##, that I can distribute on a certain length ##L## just the way I want it to. Meaning that...

Hi, I have a problem in my program and I cannot figure it out. In the last post I had a problem about some arrays, I perfectly resolved it thanks to you, but now my problem is a little bit subtle. I have a subroutine(here I'll post it has a program )that generates random numbers in order to...

I learned that dark matter distrubition is homogeneius and isotrophic in cosmic scales. I searched some galaxies dark matter distrubition.And I am actually suprised. Why cause every galaxy has a different ratio of dark matter baryonic matter distrubition. In cosmic scales baryonic...

Hello all, Is there any lower bound on the following Binomial distribution \sum_{k=floor(N/2)+1}^N{N\choose k}\epsilon^k(1-\epsilon)^{N-k} as N goes to infinity and where epsilon is less that or equal 10^-3? Thanks

I need help understanding normal distribution. I am self studying statistics to help me in my role of teaching excel as a business tool. I understand taking a data set and creating a frequency distribution. I don't understand about normal distribution. Why should any data set regardless of...

Homework Statement Random variable X is uniformly distributed on interval [0,1]: f(x)=\begin{cases} 1 & \text{ if } 0\leq x\leq 1\\ 0 & \text{ else} \end{cases} a) Find probability density function ρ(y) of random variable Y=\sqrt{X} +1 I tried like this. Is it good, if no why not...

A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions. What is the probability of getting exactly 6 questions correct on this test? The answer is: $$\binom{10}{6} (0.2)^6...