Distribution Definition and 1000 Threads

If $$p(x=1)=p(x=2)$$ where $$x$$ follows a Poisson distribution, then find $$p(x=0 ~~or~~ 1) $$. Also find $$F(x)$$In connection with the above question, I have confusion about the last part i.e., about $$F(x)$$. I can find $$E(x)$$ here, but how to find $$F(x)$$.

It is well-known that with known marginal probabilities a_{i} and b_{j} the joint probability distribution maximizing the entropy H(P)=-\sum_{i=1}^{m}\sum_{j=1}^{n}p_{ij}\log{}p_{ij} is p_{ij}=a_{i}b_{j} For m=3 and n=3, a=(0.2,0.3,0.5), b=(0.1,0.6,0.3), for example, \begin{equation}...

Homework Statement The normalized energy eigenfunction of the ground state of the hydrogen atom is ##u_{100}(\underline{r}) = C \exp (-r/a_o)##, ##a_o## the Bohr radius. For this state calculate 1)##C## 2)The radial distribution function, the probability that the electron is within a...

Homework Statement There are two stores A and B. Customers can equally enter one of the two stores, i.e., for a specific customer, the probabilities she enters store A or B both are 0.5. If the total number of customers in two stores has the Poisson distribution of parameter λ, then...

I've been asked to fit the histogram with a Poisson distribution as part of a mostly independent learning thing. The data was produced through a stochastic simulation. Can someone get me started on how I would go about finding the expected distribution? If you need additional information...

[b]. Hello, I have recently been given a course at work as someone left and they had already paid for it, unfortunately I am a bit green to electrical systems ( I only work in stores but want to learn) And my course helper, our onsite electrical man is off on long term sick! In my course I...

Dear All, I have some doubts in induced charges surface distribution.suppose their is a spherical shell and a negative charge is kept inside the shell(not at the center of shell) then induced charge distribution at inner surface of cavity is not uniform due to eccentric position of charge but...

Homework Statement Homework Equations f(x) = e-λλx/x! The Attempt at a Solution Initially I thought I could solve this problem using the Law of Memoryless. That, the solution would just be P(X <= 2). However, I was wrong. Turns out the solution is P(X <= 4.5) - P(X<= 2.5). Does anyone know why?

Homework Statement My problem is how to calculate the Shear Flow Distribution through this open cross-section. The section has a uniform thickness of 2mm and all other dimensions are on the attached picture. There is also a 100 kN downwards force applied. Homework Equations q(s) =...

Homework Statement I'm given data for 5 years of number of accidents. The problem asks about the Variance of the empirical distribution of the number of accidents per year. Homework Equations The Attempt at a Solution I'm not sure what an empirical distribution means. I wasn't...

Homework Statement A cavity at Temperature 6000k has an energy distribution corresponding to a blackbody. We make a small hole in it 1mm in diameter. Calculate the power radiated through the hole of wavelength interval between 550nm and 551nm. HINT: when dλ is small (such in this case)...

I am told that an exponential distribution is memoryless. But why aren't other distributions, such as the normal distribution, also memoryless? If I pick a random number from an exponential distribution, it is not effected by previously chosen random numbers. But isn't that also the case for...

I don't understand why roots of unity are evenly distributed? Every time when we calculate roots of unity, we get one result and then plus the difference in degree, but I think this follows the rule of even distribution and I don't understand that, it is easy to be trapped in a reasoning cycle...

Homework Statement Find the conditional distribution function and density for the random variable X defined on R given that X is in some interval I = (a,b) where P(X in I) > 0. Assume that the density and distribution for the random variable X is known Homework Equations fX|X\inI =...

This is not a homework problem. Just a curiosity. But my statistics is way rusty. Suppose a binomial probability distribution with probability p for a success. What is the expected number of trials one would have to make to get your first success? In practice, this means if we took a large...

Hi guys. Could anybody tell me how the Johnson distribution was derived? I have searched the internet but I couldn't find anything useful. Any suggested links or books will be very useful.

I have a mean mu, and an exponential distribution function. How do I use a random number, generated with a PRNG, to get a random number from the distribution? I know this is a really basic question. Please help :) Thanks

Homework Statement Two line charges, of length L/2 and carrying equal and opposite charge density ±λ, are placed on the x-axis so that their ends just touch at the origin, as shown in Figure 1. They are separated by an insulating material with negligible width. a. Find the magnitude and...

Hello, I've been looking at the derivation of the exponential function, here http://www.statlect.com/ucdexp1.htm amongst other places, but I don't get how, why or what the o(delta t) really does. How does it help? It's really confusing me, and all the literature I've looked at just...

Question: You’re 1.5 m from a charge distribution whose size is much less than 1 m. You measure an electric field strength of 282 N/C. You move to a distance of 2.0 m, and the field strength becomes 119 N/C. What’s the net charge of the distribution? (Hint: Don’t try to calculate the charge...

Homework Statement A machine fills cereal boxes, normally distributed, with standard deviation of .1 oz. What amount setting should the machine be set to if only 1% of the boxes can have less than 16oz of cereal? Homework Equations The Attempt at a Solution I am thinking that I...

Hello everyone! I'm a little confused. The Fermi-Dirac distribution is about every electron in a metal or only about the valence electrons?

Hi, I'm not sure if this has been brought up before. I'm a non-mathematician. I like to know what's the use of continuous probability distribution. Is there any use for it, is it merely a mathematical object or has it real(practical uses for it) If there are practical uses for it, what is it...

Hi, I hope somebody can help me with this one. Homework Statement Compute the Fourier Transform of the distribution x-a Homework Equations The Fourier Transform of a distribution is just the distribution evaluated with the Fourier Transform of a test function.The Attempt at a Solution See...

The Lagrangian for a point particle is just L=-m\sqrt{1-v^2}. If instead we had a continuous distribution of matter, what would its Lagrangian density be? I feel that this should be very easy to figure out, but I can't get a scalar Lagrangian density that reduces to the particle Lagrangian in...

I have a final exam in probability and I faced a question that made me think of the logic and the concept of the normal distribution. Here is the question: A food industry company imports oil in big tanks and refills bottles of different sizes with it. One of the main filling sizes is the...

Hello all, I just have a question which covers binomial distribution. Sally is a goal shooter. Assume each attempt at scoring a goal is independent, in the long term her scoring rate has been shown as 80% (i.e. 80% success rate). Question: What's the probability, (correct to 3...

1. Radial and angular distribution functions for an orbital Find the most probable value of theta and r for a 2pz orbital Homework Equations \psi _{2p_{z}} = N \textrm{cos}(\theta) r exp (-r/2) in units of a_0 The Attempt at a Solution Most probable r is when \textrm{d/d}r (P(r))=0...

Homework Statement Repeatdly roll a fair die until the outcome 3 has accurred on the 4th roll. Let X be the number of times needed in order to achieve this goal. Find E(X) and Var(X) Homework Equations The Attempt at a Solution I am having trouble deciphering this question...

If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution? I tried to do this with the sum of bernouli variables and...

Homework Statement Let X_n \in Ge(\lambda/(n+\lambda)) \lambda>0. (geometric distribution) Show that \frac{X_n}{n} converges in distribution to Exp(\frac{1}{\lambda}) Homework Equations I was wondering if some kind of law is required to use here, but I don't know what Does anyone know how this...

I want to derive this equation: V(r) = \frac{1}{\epsilon_0} [\frac{1}{r} \int_0^r \! r'^2 \rho(r') \, d r' + \int_r^{\infty} \! r' \rho(r') \, d r' ] of a spherical charge distribution. I can do it with the general integral definition of the electrostatic potential (which is basically...

While I get the coherent and incoherent scattering process that leads to the bragg diffraction condition, I don't really understand the physical mechanism behind the transmission and reflection. Now, as I understand it, the bragg diffraction condition is satisfied only for one or two particular...

Isn't the point of center of mass is where the masses on both sides are equally distributed? Why is it not the case here?

I have a rainfall (mm) vs. year plot of a catch basin (see Excel file below) and I would like to get it's frequency curve. But before that, I need to fit certain distribution models (i.e. log-Pearson Type III and Gumbel Distributions) to my plot to be able to know the fittest model that I can...

John is going to eat at at McDonald's. The time of his arrival is uniformly distributed between 6PM and 7PM and it takes him 15 minutes to eat. Mary is also going to eat at McDonald's. The time of her arrival is uniformly distributed between 6:30PM and 7:15PM and it takes her 25 minutes to eat...

Homework Statement hi, so I've got this distribution function: f(z,p,t)=\frac{1}{2\pi\partial z\partial p}exp(-\frac{[z-v(p)t]^2}{2\partial z^2})exp(-\frac{[p-p_0]^2}{2\partial p^2}) where: v(p)=v_0+\alpha(p-p_0) v_0=\frac{p_0}{m\gamma_0} \alpha=\frac{1}{m\gamma_0^3} I have to...

Homework Statement We are given a sample of size 100. After some tests (histogram, Kolmogorov) we deduce the sample X is distributed uniformly. The next task is to presume the parameters are equal to values of your choice, and test if such hypothesis is true. Homework Equations The Attempt at...

Is the most stable/likely configuration of protons in heavy nuclei that of being evenly distributed throughout the nucleus? As opposed to something like a spherical distribution?

I have one question, I am sorry if it's stupid or something. So, when we write down the Maxwell's distribution, we integrate over the spectrum of velocities... But that is from 0 to infinity.. (or minus infinitiy to infinity nevermind) Is there any way someone can cut-off the above? Since we...

I am doing some problems from a practice final and would like to know if the following problem has mistakes in the way it is written. We are supposed to apply a corollary that doesn't seem to have any relevance in this context. It is throwing me off. **Problem statement:** Suppose that $X$ ~...

Hi, The question is: http://puu.sh/5GX2G.jpg http://puu.sh/5GX2G.jpg I am not exactly sure what the question is asking. Here is the answer/solution: http://puu.sh/5GX68.png But I am not sure what is going on. Could someone please explain what exactly the question is asking...

$$f(y) = \begin{cases} 0& \text{for }y< 0,\\ 2y& \text{for }0 ≤ y ≤ .5,\\ 6-6y& \text{for }0.5 < y ≤ 1, \\0& \text{for } y > 1\end{cases}$$ (1) Find cumulative distribution function, F(y) $$F(y) = \begin{cases} 0& \text{for }y< 0, \\\int_0^y 2t dt = y^2 & \text{for } 0 ≤ y ≤ .5,\\.5^2+...

A random variable X drawn from a uniform [0,3] distribution and a random variable y is independently drawn randomly drawn from a uniform [0,4] distribution. The joint probability density f(x,y) is also uniform, with support given by 0 ≤ x ≤ 3, 0 ≤ y ≤ 4. Find the probability for the sum of two...

$$f(y) = \begin{cases} \int_0^y\frac1\beta e^{\frac {-t}\beta}dt = -e^{\frac {-y}\beta}+1 & \text{for } 0 ≤ y < ∞,\\ 0& \text{for } elsewhere\end{cases}$$ P(Y>3) = 1 - P(Y ≤ 3) = 1 - (-e^{-3/beta}+1) = .1353 When I take log to both sides, I get 3.453. When I take ln to both sides, I get...

Hello, I am working on the two point correlation function in dark matter haloes. Right now i need to create an array of rundom numbers to compute the estimators. My question is: How can i create a random distribution of points in the unit sphere (having in mind its curvature). I...

By Definition, Let ν be a positive integer. A random variable Y is said to have a chi-square distribution with ν degrees of freedom if and only if Y is a gamma-distributed random variable with parameters α = ν/2 and β = 2. By Thm, If Y is a chi-square random variable with ν degrees of freedom...

With mean = 2 with exponential distribution Calculate E(200 + 5Y^2 + 4Y^3) = 432 E(200) = 200 E(5Y^2) = 5E(Y^2) = 5(8) = 40 E(4Y^3) = 4E(Y^3) = 4(48) = 192 E(Y^2) = V(Y) + [E(Y)]^2 = 2^2+2^2= 8 E(Y^3) = m_Y^3(0) = 48(1-2(0))^{-4} = 48 is this right?

The amount of time to finish a operation has an exponential distribution with mean 2 hours Find the probability that the time to finish the operation is greater than 2 hours. My thinking is to integrate the exponential probability function. After integrating it, I got -e^{-y/2} + 1 , 0 ≤ y...

Hi, After adding a wire across a circuit to section off part of the load in the form of a short circuit, I am still seeing a couple of milliamps flowing through the load. Is this due to the fact that the wires used to create the short circuit will have a small amount of resistance, hence...