Distributions Definition and 309 Threads

This is a vague question and I apologize in advance for not being able to explain it better. I'm combining r.v.'s from different populations (distributions). The resulting population can be thought to come from a mixture distribution. I think another way of describing the resulting...

There are some really really good treatises out there on fractional crystallization, and I'm ploughing through them one at a time. One very basic thing has me confused, though: If you have 1 liter of water at 100C, it will dissolve 455g of NaCO3 or 1150 of KCO3, or pretty much any linear...

When considering tempered distributions, I am only aware of the definition of test functions of a real variable. However, is it okay to use test functions of a complex variable z that are analytic in a strip that includes the real axis? (of course they still must fall off fast enough as the...

I am confused about when you can use the formula ##\dfrac{q_{enc}}{\epsilon_0} = \Phi## for flux. Is it only when you have a closed surface with point charges? What if you have a closed surface with a non-point charge?

Why are there so many physical processes which are described (with more or less accuracy) by a normal distribution?

I'm an oldie and not well-versed in the modern formalism used in stochastic calculus, so please bear with me. I'm aware of Levy's characteristic function for stable distributions, though not well-versed in its practicalities. I have read that for alpha=2 the stable distribution is Gaussian...

Hi everyone, the question is simple: is \mathcal{S}'\left(\mathbb{R}^3\right) a first countable topological space ? I have no idea, honestly. (The question has occurred to me from a statement of Rafael de la Madrid in his PhD thesis when discussing the general rigged Hilbert space formalism...

Hello, I am trying to understand what makes estimating the posterior distribution such a hard problem. So, imagine I need to estimate the posterior distribution over a set of parameters given the data y, so a quantity P(\theta|y) and \theta is generally high dimensional. The prior over...

Homework Statement As the title indicates. I'm given two independent exponential distributions with means of 10 and 20. I need to calculate the probability that the sum of a point from each of the distributions is greater than 30. Homework Equations X is Exp(10) Y is Exp(20) f(x) =...

Hi, It has been a long time since I have worked with pdfs so perhaps someone can help. According to Wikipedia (http://en.wikipedia.org/w/index.php?title=Chi-squared_distribution#Additivity) the pdf of the addition of n independend Chi_squared distributed R.V.s is also Chi_squared distributed...

Forgive me if this is a silly question, but here goes: Say you have two unrelated distributions (A and B) with known means and standard deviations. How would you determine the probability of any single value of A being greater than any single value of B? The easiest example I can come up...

If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? So this problem is hard to wrap my head around. I'm probably wrong on many counts, here's what I'm doing: Two fair dice are rolled 10 times but this question only...

Two independent random variables X and Y has the same uniform distributions in the range [-1..1]. Find the distribution function of Z=X-Y, its mean and variance. =Using change of variables technique seems to be easiest. fX(x) = 1/2 fY(y) =1/2 f = 1/4 ( -1<X<1 , -1<Y<1) Using u =x -y...

My calculator isn't at all happy running the likely hood of finding a prime at 10,000 digits. Since there is a correlation very close to 1/2 the number of primes for each increase of 1000 digits after 1000 digits I was thinking I could just use, 1/2^(n/1000)×1151.3 = probability of finding a...

Hi everyone, Suppose I have two samples that can be described by an observable. Call it x. x can take on any value from 0 to infinity. The distribution of values of x for sample 1 can be described by the normalized probability distribution f(x). The distribution of values of x for...

The potential due to a polorized distribution is given by: V( \vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \int _{V} \frac{ \hat{r} \cdot \vec{P} ( \vec{r}')}{r^{2}} dV After working some voodoo math, this is worked into the form V = \frac{1}{4 \pi \epsilon _{0}} \oint _{S} \frac{1}{r} \vec{P}...

Suppose I have a Gaussian probability distribution: N_{A}(0,1). A set of values are generated from this distribution to which an arbitrary amount of Gaussian noise, say N_{B}(0,0.5), is added and then the N_{B} values sorted from lowest to highest. These are then digitised by assigning 0...

Homework Statement Let X1, X2,...,X16 be a random sample of size 16 from N(μ=50, σ2=100) distribution. Find P(Xbar > 50 + .6505(s)) Homework Equations Z= (xbar - μ)/(σ/√n) The Attempt at a Solution So I know the solution of this problem is given by P( T(15 d.f.) > 2.602 )...

derive the MGF hence find their mean and variance 1 weibull distribution 2 pareto distribution 3 lognormal distribution

In shipment A, there are 990 correct and 10 faulty units. In shipment B, there are 1940 correct and 60 faulty units. 100 units out of each shipment is inspected. Calculate with an APPROPRIATE approximation the probability of finding five or more faulty units. Emphasis from book, not me...

fXY(x,y)=2 if 0<x<1 and x<y<1, 0 for other intervals I have to calculate: P((x>0.5)π(y<0.5)). I think it 0 but I am not sure because in all other exercises I've made the surfaces intersect each other. Like in fig 1 for P((x<0.5))π(y<0.5))=integral from 0 to 0.5 from integral from x to 0.5 from...

Hi I'm currently studying for my second year engineering exams, and I'm struggling with distributions. Unfortunately I missed most of the statistics lectures in my math course (something I massively regret now) and the lecture slides aren't annotated enough to give me any clue what is happening...

Hi everyone, I would like to know if this stament is true or not. I have two variables u,v both of them distributed as normal distribution with mean 0 and variance a^2. Is it true that the expected value of uv is a^2 ? Thanks

calculating electric fields due to continuous charge distributions? a question I came across doing some electric field questions, and the answer was really confusing. Homework Statement Charge is distributed along a linear semicircular rod with a linear charge density λ as in picture...

I have this question: and I'm a little confused. To calculate joint distributions in the earlier questions i was using:P_{(\xi1,\xi2)}(x1,x2)=P_{(\xi1)}(x1)P_{(\xi2)}(x2)But that would mean that if:P_{(\xi1,\xi2)}(2,0)=0\ either\ P_{(\xi1)}(2)=0\ or\ P_{(\xi2)}(0)=0which can't be true in...

Hi, I have a general concept question. I am working with finding complete sufficient statistics of distributions. Sometimes I need to condition some function of a parameter on a sufficient statistic, using basically Rao-Blackwell, but my trouble is in finding the conditional distributions...

Homework Statement A certain manufacture advertises batteries that will run under a 75 amp discharge test for an average of 100 minutes, with standard deviation of 5 minutes. a. find an interval that must contain at least 90% of the performance periods fr batteries of this type. b...

Is it possible to combine statistics from two distributions for the same parameter. For example I have one distribution for X from population A and a second distribution for X from population B. I want to assume all data is from the same population. I have calculated UTLs(Upper tolerance...

Over in the Quantum Physics forums, we occasionally have threads involving rigged Hilbert space -- a.k.a. Gel'fand triple: ##\Omega \subset H \subset \Omega'## where ##H## is a Hilbert space, ##\Omega## a dense subspace thereof such that certain unbounded continuous-spectrum operators are...

Homework Statement Positive charge +Q is distributed uniformly along the +x axis from x=0 to x=a. Negative charge - Q is distributed uniformly along the +x axis from x=0 to x=-a. A positive point q lies on the positive y axis, a distance y from the origin. Find the force (mag and dir.) that...

A pdf is of the exponential family if it can be written $ f(x|\theta)=h(x)c(\theta)exp(\sum_{i=1}^{k}{w_{i}(\theta)t_{i}(x))}$ with $\theta$ a finite parameter vector, $c(\theta)>0$, all functions are over the reals, and only $h(x)$ is possibly constant. I would like to show the binomial...

Hello, I am trying to quantify the difference between two discrete distributions. I have been reading online and there seems to be a few different ways such as a Kolmogorov-Smirnov test and a chi squared test. My first question is which of these is the correct method for comparing the...

Homework Statement We have an interval [0,1], which we divide into k equally sized subintervals and generate n observations. Let's call the number of observations which falls into interval k_i, X_i. What distribution does X_1 have? Now we define Y_i=X_i/n. Derive the Expected value...

1. A particular nuclear plant releases a detectable amount of radioactive gases twice a month on the average. Find the probability that at least 3 months will elapse before the release of the first detectable emission. What is the average time that one must wait to observe the first emission...

1. If a pair of coils were placed around a homing pigeon and a magnetic field was applied that reverses the earth’s field, it is thought that the bird would be disoriented. Under these circumstances it is just as likely to fly in one direction as in any other. Let θ denote the direction in...

Homework Statement I was given two problems and required to calculate some statistics/parameters for them. They are: 1) The Vancouver Island Marmot is one of Canada’s most endangered species; there are currently only 63 animals left on the Island. To maintain the population, geneticists...

Homework Statement Consider the gaussian distribution ρ(x) = Aexp[(-λ^2)(x-a)^2] , where A, a, and λ are positive real constants. (a) Find A such that the gaussian distribution function is normalized to 1. (b) Find <x> (average; expected value) , <x^2>, and σ (standard deviation). (c)...

In the page that I attached, it says "...while at the continuity points x of F_x (i.e., x \not= 0), lim F_{X_n}(x) = F_X(x)." But we know that the graph of F_X(x) is a straight line y=0, with only x=0 at y=1, right? But then all the points to the right of zero should not be equal to the limit of...

Hello, I had a question about data which is represented by a fractal distribution. I know that the linear regression lies in the plot of log(N) vs. log(x) for which the ratio represents the fractal dimension as the limit of x going to infinity. However, how would one get the representative...

Homework Statement A committee of 16 persons is selected randomly from a group of 400 people, of whom are 240 are women and 160 are men. Approximate the probability that the committe contains at least 3 women. I just want to know if it's hyper geometric or binomial. I suspect it's hyper...

Please help me find some references where public bus headways are described(modeled) as gaussian processes. Best Regards

1. Suppose X~B(5,p) and Y~(7,p) independent of X. Sampling once from each population gives x=3,y=5. What is the best (minimum-variance unbiased) estimate of p? Homework Equations P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}The Attempt at a Solution My idea is that Maximum Likelihood estimators are...

[SIZE="4"][FONT="Times New Roman"]Let X_1, X_2 \sim Exp(\mu) and Y = min(X_1, X_2) then find E[Y]. My attempt is as follows: $$E[Y] = E[Y/X_1<X_2]P(X_1<X_2) + E[Y/X_1>X_2]P(X_1>X_2) \\ = \frac{1}{2} (E[X_1/X_1<X_2] + E[X_2/X_1>X_2] ) \\ = \frac{1}{2} (1/\mu + 1/\mu) \\ = 1/\mu$$ But, we know...

If we have a uniform distribution on [0,x]...then the pdf is 1/x right? But what if we have [0,x)? Do we still have the same pdf? Thanks in advance.

What is a measure of "jointness" of a joint distribution? Correlation?

Dear all, I hope someone can help me. I have two experimental groups, A (n=5) and B (n=8) containing biological samples. The samples are used to estimate my parameter of interest, θ. I do this with Markov-chain Monte-Carlo, which gives me a posterior distribution of θ for each of my samples...

Hi, Again: I'm trying to show that, given a 3-manifold M, and a plane field ρ (i.e., a distribution on TM) on M, there exists an open set U in M, so that ρ can be represented as the kernel of a differential form w , for W defined on U. The idea is that the kernel of a linear map...

I've been trying to code an algorithm to compute the convolution of two probability distributions. using the FFT. This relies on the "convolution theorem": (p*q)[z] = FFT^{-1}(FFT(p) \cdot FFT(q)) However, when I test it using the distributions p={0.1, 0.2, 0.3, 0.4} q={0.4, 0.3, 0.2, 0.1}...

Hi there, I'm working on a simulation of the travel patterns of cars. There are many variables and conditional probabilities in the model. My question is, is there anything wrong with fitting all non parametric distributions to variables (both continuous and discrete)? The software I'm...

Homework Statement We have an urn with 5 red and 18 blues balls and we pick 4 balls with replacement. We denote the number of red balls in the sample by Y. What is the probability that Y >=3? (Use Binomial Distribution) Homework Equations The Attempt at a Solution Okay, so we...