Distributions Definition and 309 Threads

I am trying to generate 2 normal random distributions (x1,...,xn) (y1,...,yn) that have a predefined degree of correlation between them. The constrain is that I am trying to have the same mean and stdev for both of them.

(\Triangular" distributions.) Let X be a continuous random variable with prob- ability density function f(x). Suppose that all we know about f is that a </= X </= b, f(a) = f(b) = 0, and that there exists a value c between a and b where f is at a maxi- mum. A natural density function to...

Hi Everyone, I am analyzing real data using fast-fourier transforms (FFT) in Matlab. The FFT magnitude spectrum show some background noise floor with several sharp spurs popping up high out of the background noise. I need to figure out conclusively which of these spurs are correlated with...

where can I read about distributions and the delta function. esp. to solve singular integrals. I have seen that you could write 1/x = \delta (x) + P.V (1/x) and all that stuff.. where can i read about it ...

Homework Statement A small, thin, hollow spherical glass shell of radius R carries a uniformly distributed positive charge +Q, as shown in the diagram above. Below it is a horizontal permanent dipole with charges +q and -q separated by a distance s (s is shown greatly enlarged for clarity)...

[SIZE="2"]Warning: I've only taken one stats class, back as an undergrad (though it was a very fast-paced class designed for mathematicians). My understanding of all things statistical is consequently weak. I'm trying to design a program to accurately time functions. The functions themselves...

Can someone please help with the method of how to solve this problem... Question: Three balls are thrown at random into 5 bowls so that each ball has the same chance of going into any bowl independently of wherever the other 2 balls fall. Determine the probability distribution of the...

Don't know if this is the right place to post it, but oh well:smile: Homework Statement A one-sided conductor plate with negligible thickness and infinite dimension is charged to a voltage of V via electrostatic induction. Assuming charge is distributed evenly on the surface of the...

Is it correct to say that independent random events (additively) lead to a normal distribution, and dependent random events (multiplicatively) lead to a power law distribution? The following might be trivial, but it was quite interesting to find for me, someone with a very limited knowledge...

Hey... I have a quick question for you guys about electric potential. I have a spherical shell with a constant charge distribution. The total charge(Q), along with the shell's radius is given. Also, V(infinity) is defined to be 0 in this case. I'm told to find: a. The potential at r = the...

Homework Statement Find the charge and current distributions for V(r,t)=0 A(r,t) = -1/(4*pi*epsilon) q*t/r^2 r-hat Homework EquationsWe know E=1/(a*pi*epsilon) q/r^2 rhat B = 0 The Attempt at a Solution What formula do I use? We know grad x B = mu*J +mu*epsilon dE/dt Would this suffice...

Let X,Y~U(0,1) independent (which means that they are distributed uniformly on [0,1]). find the distribution of U=X-Y. well intuitively U~U(-1,1), but how to calculate it using convolution. I mean the densities are f_Z(z)=1 for z in [-1,0] where Z=-Y and f_X(x)=1 for x in [0,1], now i want to...

On a multiple guess exam, there are 3 possible answers for each of the 5 questions. What is the probability that the student will get four or more correct answers just by guessing? Is this hypergeometric or binomial?

I want to test if one Poisson distributed result a is large than another one b. I don't know much about statistics, but I understood the Wiki article about testing normal distribution however they need the number of samples there. Basically I measure two Poisson distributed variables, I get two...

I'm not sure I understnad what is a marginal distribution, but i need to show that if F1,F2 are one dimensional cummulative distribution functions then I(x,y)=F1(x)F2(y) has F1 and F2 as its marginal distributions. well if I(x,y)=P(X<=x,Y<=y) and if X and Y are independent, then it equals...

[SOLVED] Arrival,wait and service distributions Hello everyone, I am doing simulation of crowd movements and behaviors. I have developed a very flexible simulator platform (it has taken a year) which can simulate almost 100,000 pedestrians in real time. I wanted to check statistical...

i was doing some exercises nut I'm not sure if my answers are correct 1) X~B(5,0.25) i have to find: a) E(x^2) and my answer was 2.5, is this correct? b) P(x(>or=to)4) and my answer was 0.0889, is this correct? 2) X~Geom(1/3) i have to find: a) E(x) my answer is 1/3 b) E(x^2) c)...

What kind of tangent distributions are not integrable? Is there concrete examples with two dimensional non-integrable distributions in three dimensions? When I draw a picture of two smooth vector fields in three dimensions, they always seem to generate some submanifold, indicating integrability.

Hello all. With the standard caveat that my background is neither in math nor science, I've nonetheless been conducting some further independent study in various areas of statistics that are of interest to me. With the foregoing as background, I'm trying to appreciate the material...

Hey, I'm new to all this so cut me some slack, but have been trying to work through some questions, and I can't seem to find answers to these questions... Or atleast find the confidence that my answers/working is correct... 1. (Exponential Distribution) Telephone calls arrive at the...

In the quantum version of the symmetric infinite well, the energy eigenvalues are, in principle, well-determined. Why would the momentum then have a spread or distribution for a given energy eigenvalue i.e. \phi(p) = 1/(2\pi\hbar) \int_{-a}^{a}dx u_n (x) e^{-ipx/\hbar} where u_n is the...

Is there any way to calculate the Fourier transform of the functions \frac{d\pi}{dx}-1/log(x) and \frac{d\Psi}{dx}-1 (both are understood in the sense of distributions) i believe that these integrals (even with singularities) exist either in Cauchy P.V or Hadamard finite part...

Hello I would like to hear your opinions on the normality of scores on an IQ test. The test had 30 questions and apart from the general IQ score separate subtest scores such as mathematics, verbal and spatial IQ were also calculated. Here is a list of results that were obtained from the...

A group of students wish to determine how long, on average, customers are waiting in line at a supermarket before being served. The students conduct trials and record the times taken. They found that they were kept waiting for an average of 7 minutes. If a customer goes to that same...

Hi all, I realize this is not directly a homework question but it is related to the year 12 applicable mathematics course and given the forum area is called "Homework & Coursework Questions" I assumed this was the place :) I have an in-class EPW (extended piece work or whatever you want to...

Homework Statement The problem: An airline always overbooks, if possible. A particular plane has 95 seats on a flight and the airline sells 100 tickets. If the probability of an individual not showing is 0.05, assuming independence, what is the probability that the airline can...

Suppose I had a random variable, X, that followed a Gamma distribution. A Gamma distribution can be defined as \Gamma(\alpha,\beta) , where \alpha and \beta are the 'scale' and 'shape' parameters. Now suppose if \alpha was a random variable, say following a binomial distribution, how would...

If X and Y are gamma distributed random variables, then the ratio X/Y, I was told follows a beta distribution, but all I can find so for is that the ratio X/(X+Y) follows a beta distrinbution. So is it true that X/Y follows a beta distribution?

I am not sure which distribution this is: there are N animals in a forest, we don't know N but would like to estimate it... so, I need to select a model (distribution) ps: i am trying to avoid Normal distribution...

Is it possible to have a distribution of a rv with infinite mean? Techinically, mean is the expected value so... if the integral/summation does not converge? Does anyone have a specific example of such a distribution? Thanks!

X1, X2, X3 are independent gaussian random variables. Y1 = X1+X2+X3 Y2 = X1-X2 Y3 = X2-X3 are given. What is the joint pdf of Y1,Y2 and Y3 ?

I'm having a problem evaluating a distribution- Suppose X and Y are Chi-square random variables, and a is some constant greater than 0. X and Y are independent, but not identically distributed (they have different DOFs). I want to find P(X>a,X-Y>0). So I use Bayes' theorem to write...

I have three sets of data that I’ve used to create three Gaussian distributions which have different means and standard deviations. The data sets are also correlated as the data is dependent on time. I want to compare the sum of two distributions with the sum of three distributions to find which...

I was reading about the derivation of the Heisenberg Uncertainty Principle and how Heisenberg used Gaussian Distributions to represent the uncertainty of position and momentum in his calculation. Why is it that Gaussian Distributions were used? There are many different types of distributions...

Consider a poisson process one (P1) with a frequency 'a' and if it happens 'k' times you get (e^-a)(a^k)/k! and then you have another posssion processs that happens in the same time frame of P1 called P2 with a frequency of 'b' and if it happens 'z' times you get (e^-b)(b^z)/z! So what is...

I think Schwartz proved that 2 distributions couldn,t be multiplied..but why?..if we had 2 delta functions then their "product" is: \delta (x-a) \delta(x-b)=f(a,b,x) so i have obtained the product of 2 Dirac,s delta considering that delta is a distribution is not this a contradiction...

I was wondering about this when playing bridge with my friends. I understand, that one player can be dealt C^{13}_{52} different distributions of the cards. But how to calculate the probability, that all players will get the same cards?

I'm not too sure where to post this so feel free to move it :) Anyway I'm hoping someone could explain the answer of this problem to me (I would ask my lecturer but he's conveniently away for the week for a meeting). Suppose X and Y are iid continuous random variables with density f...

If you have a problem that involves some distribution, how do you know which one to use? The ones we covered so far are: Binomial Negative Binomial Hypergeometric Poisson Distribution Poisson Process

Hiya guys, I just have what I'm sure is a simple question about statistics, but I can't seem to find it anywhere ... I was wondering, when finding the standard deviation of a sample mean, why do you divide the population standard deviation by the square root of n? I'm not really sure why...

Hello. My textbook says that a Gaussean surface must be carefully chosen so that a point charge (or point charges constituting a discrete charge distribution) does not lie ON it, as otherwise the electric field at the location of the charge would be infinite and hence, it would not be possible...

How would the probability distribution (|psi|^2) look for a Newtonian particle if it were confined in a box?

Basically, I'm having some difficulty grasping some of the concepts in probability. ..At first I was writing details of what my lecturer has given me, but really I can't make much sense of it and it'd be foolish to type it all out here. The jist of work is really just as follows; we've...

Hi all, Does anybody know some reference (even internet one) that explains in detail the derivation of Maxwell´s velocity and/or energy distribution on an ensemble of atoms/molecules ? References to Fermi-Dirac distributions and Bose-Eisntein´s are also welcome. Best Regards, DaTario...

The following is crude derivation demonstrating how a distribution such as the normal distribution is simply one distribution that stems from a family of similar distributions. I originally was going to post this in the new Independent Research forum but the moderator thought it was...

Hi, I am new here, so I apologize if my post is not appropriate for this forum. I have a background in chemical engineering and used to be really good at math, but after many weeks of trying to solve my problem, I am about ready to admit defeat. I hope someone here can help me out. My goal...

Given a time series Yt, how can you decide what distribution the values obey, if any? In particular, is there a way to make sure the time series obeys a Gaussian distribution? Thanks, Frank

Ok, this might seem like either a really idiotic question or a really profound one. Consider a probability distribution. I'm picturing a normal distribution, is it meaningful to be able to build up a final probability distribution from a set of narrower probability distributions? Ok...

How does one go about actually computing various statistical tables, rather than looking them up? Things of interest at the moment are the cumulative distributions and their inverses, for the standard normal and both central and noncentral chi squares.

Okay so say we have charge Q on a 2-sphere of radius R then the charge distribution will be rho=(Q/2piR^2)delta(r-R), which gives Q when integrated over space. 1) So my question is, what does this say about rho? To me, it says that rho is zero everywhere except on the surface of the sphere...