Distribution Definition and 1000 Threads

Homework Statement The technical specification of a particular electrical product states that the probability of its failure with time is given by the function: f(t) = 1 - ke^(-t/t0) if 0 < t < tmax f(t) = 0 if t > tmax where t is the time of service...

Let $X$ = the time between two successive arrivals at the drive-up window of a local bank. $X$ has an exponential distribution with $\lambda = 2$. That is the probability density of $X$ is $f(X | \lambda) = \lambda e^{-\lambda x}, X > 0 $ with $\lambda = 2$. Compute the following: a) The...

I want to create an array of numbers between 0 and 0.1 where the points are clustered around an arbitrary point x1 (0 < x1 < 0.1). I want the points to get exponentially closer together near x1 from either side and and get further apart towards the outer limits. I am using MatLab and was trying...

What is the distribution of energy and angle of backscattered electrons from a few MeV heavy ions beam? Someone telled me the energy obeys landau distribution, but I don't know what's the most probable energy.

Hi. I normally can solve poisson distribution questions with ease. But this one question had me thinking for hours on end with no solution. It would be great if someone can help me. QN: The number of incoming calls per minute, X, to a telephone exchange has a Poisson distribution with mean 2...

Problem: McBurger’s drive-thru has only one service window and serves an average of 2 customers every 5 minutes. 70% of customers order drinks from the drive-thru. The manager monitors the employee at the drive-thru for the next 3 hours. He will give the employee a raise if exactly 20 customers...

Hey all, So I have a small convergent nozzle that I'm modelling in Abaqus and I'm wondering how I could work out the pressure distribution so I can apply the correct load. The problem is I only know the pressure being fed to it by air compressor. Is there a way to use Bernoulli s or some other...

Could anyone explain in laymen terms what really the beta function does as said in Beta Function:https://en.wikipedia.org/wiki/Beta_function .I know that gamma function is used to find the factorial of real numbers but when it comes to beta function I can't get what really beta function does.I...

Homework Statement Suppose that diastolic blood pressures (DBPs) for men aged 35-44 are normally distributed with a mean of 80 (mm Hg) and a standard deviation of 10. What's the probability that in a random sample of 5 subjects, 4 or more have DBPs more than 90? Homework EquationsThe Attempt...

Homework Statement Customers arrive in single server queue to be serviced according to Poisson process with intensity 5 customers an hour. (a) If the customers begin to arrive at 8am, find the probability that at least 4 customers arrived between 9am and 10am. (b) Find the probability that the...

Hello, I am stuck at this exercise: 1. Homework Statement X ~ U(0, a), a > 0 and Y = min(X; a=2). - Find the cumulative distribution function of Y -Is the variable Y continuous ? Homework Equations 3. The Attempt at a Solution [/B] The density function for X is f(t)= 1/a if 0≤t≤a , 0...

Hi comunity! I need to make a code o a normal distribution of velocities, starting whit a random secuence uniformly distributed between [0,1]. I am using FNT95, with Plato. I want to obtain a ''for'' bucle with I=1,N for the velocities. It is importan for the distribution to have sigma defined...

Given: Assume that f (x) is continuous at x = 0 and vanishes as x→±∞. Hint. Replace x by y/n and take lim n→∞ before integrating. I apply the hint and get $ \frac{1}{\pi}\int_{-\infty}^{\infty} \,{\lim_{{n}\to{\infty}}}{\frac{sin y}{y}} \,dy $ For the limit, as n -> ${\infty}$ , y -> 0. By...

Hello! I encountered this simple model for drug distribution in a textbook, but was not able to come up with the solution myself. It's been bothering me way too much past two days... Perhaps more so because of the "Equation 7-1 is easily solved" part. Hints/help would be much appreciated...

dE = ke(dq/r2) How to change to complicated equation in the following picture?

Since most planets in the earliest stages of formation are very hot and fluid, why is it that we find on Earth areas where there are substantial deposits of heavier elements - gold, uranium, etc in the crust? Intuition suggests that these relatively rare elements would become widely dispersed...

Homework Statement P is the probability that a person aged x years will die in a year. Find the probability that out of 5 men A,B,C,D and E, each of x years, A will die in the year and be the first to die. Homework EquationsThe Attempt at a Solution I fixed A in the first place with...

Given five data points (minimum, 25th percentile, 50th percentile, 75th percentile, maximum), do I have enough information to be able to construct what a normal (Gaussian) distribution would look like? I have no data on any other statistical information (population size, mean, median, mode...

Homework Statement Find P(X>130) where P(X > 130) = 1 − Φ( (130 − µ)/σ ) Homework Equations Φ is the normal distribution density function: http://en.wikipedia.org/wiki/Normal_distribution The Attempt at a Solution This is pretty simple to use in R if one knew how to. I get a ghastly incorrect...

Hello all! I'm hoping you will be able to direct me to sources of raw income1 / employment data. Hopefully this thread can be a help to others who have similar needs in the future, as well. (I did a quick search for a similar thread and didn't find anything - please correct me if I'm wrong.)...

Homework Statement I have to prove that ## \int e^{\frac{x^2}{-2}}dx ## from +∞ to -∞ = ##\sqrt{2\pi} ## Homework Equations N/A The Attempt at a Solution My GSI went from 1) ## \int e^{\frac{x^2}{-2}}dx ## from +∞ to -∞ = ##\sqrt{2\pi} ## to 2) ## (\int e^{\frac{x^2}{-2}}dx)(\int...

Homework Statement In a study to estimate the proportion of residents in a city that support the construction of a new bypass road in the vicinity, a random sample of 2025 residents were polled. Let X denote the number in the sample who supported the proposal. To estimate the true proportion in...

Homework Statement The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 95 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2...

Hello! Dr. David Tong, in his statistical physics notes, derives the Boltzmann distribution in the following manner. He considers a system (say A) in contact with a heat reservoir (say R) that is at a temperature T. He then writes that the number of microstates of the combined system (A and R)...

Homework Statement Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)2/σ2. The Attempt at a Solution I honestly have no idea where to begin with this problem. Any ideas?

So here is my problem. I am running a "Biggest Loser" weight loss contest at work. My biggest challenge in these contests is keeping the people that are falling behind motivated. To solve this, I would like to spread the winnings across all participants that lose weight not just the biggest...

A negative charge cloud distribute as a ellipsoid and a positive point charge situated at the centre of the ellipsoid.What should be the dipole moment of charge distribution.I mean, if the negative charge distribution is spherical and positive point charge at the centre then surely dipole moment...

Homework Statement The life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential distribution with a mean of 0.6 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if...

Homework Statement For a plasma containing two ionic species with opposite charges but the same density ##n_{\infty}##, calculate the radial distribution functions ##g_{++}(r), g_{-+}(r), ##where ##n_{\infty}g_{ij}(r)## is the conditional probability density for finding a particle of type ##i##...

Homework Statement A cylindrical distribution of charge ρ = α/sqrt(r) where α = 2 µC/m^(5/2) extends from 0 cm to 9.3 cm (has radius 9.3 cm). Concentric with this is a dielectric shell with k = 5.44 of inner radius 16.6 cm and outer radius 24.9 cm. What is the electric field at 3.53 cm, 12.6...

Hi all Maybe a quick question! After the big bang and inflation, a little while later there is the mass annihilation event where 10 billion matter particles and 10 billion anti matter particles annihilate, sending out energetic photons. For each 10 billion annihilation events there is one...

Homework Statement In thermal equilibrium, the particle in a gas are distributed in velocity space according to the Maxwell distribution f(v) = A*exp(-mv^2/(2KT)) What is the average velocity ? What is the most probable velocity ? Homework Equations <v> = ∫∫∫vf(v)d3v = (0 to infinty)...

I have one dimensional binned data that has a peak to which I need to fit a distribution, such as Gaussian or Lorentzian, that is described with four parameters, height, width, centroid position and the background. The problem is that the counts per bin are low and the peak is only 5-6 bins wide...

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...