Distributions Definition and 309 Threads

I have a set of data points {xi,yi} where each yi is a Gamma distributed variable where both the shape k and scale \theta depend on i. I then fit the data points with a power law model y=a(x)b. I would like to know the probability distributions for the fit parameters a and b. Is...

Homework Statement Let \Omega = {w1, w2, w3}, P(w1) = 1/3, P(w2) = 1/3, P(w3) = 1/3, and define X, Y, Z as follows: X(w1) = 1, X(w2) = 2, X(w3) = 3 Y(w1) = 2, Y(w2) = 3, Y(w3) = 1 Z(w1) = 3, Z(w2) = 1, Z(w3) = 2 (a) Show that these 3 random variables have the same distribution. (b) Find the...

I'm trying to understand why various statistical distributions are so common. For the most part, all I can find online is how to calculate and manipulate them... I did finally find a couple of refs that helped with Gaussians, this being one: http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf"...

Homework Statement Problem A: A random variable T is selected from a uniform distribution over (0,1]. Then a second random variable U is selected from a uniform distribution over (0,T]. Determine the probability Pr(U>1/2). Problem B: Suppose 3 identical parts are chosen for inspection. Each...

Homework Statement [PLAIN]http://img695.imageshack.us/img695/7551/unledsi.png Homework Equations The Attempt at a Solution I get E[u]=1/3 and E[V]=1, can't get E[UV] to be correct as I do not get the required answer, any help would be greatly appreciated! thanks!

Homework Statement Consider a Poisson process for which events occur at a rate of 2 per hour. (a) Give the probability that the time until the first event occurs exceeds 2 hours. Use an exponential distribution to find the probability.Homework Equations The Attempt at a Solution \lambda = 1/2...

How can I prove that the any linear combination of multivariate normal distribution is also normal? I can prove it but I'm not sure that this is right or not. The point of my proof is as follows. --- The X and Y has the same dimensional random vector, and each random vector is...

Let X1,...,Xn be independent, identically distributed random variables with exponential distribution of parameter λ. Find the density function of S = X1+...+Xn. (This distribution is called the gamma distribution of parameters n and λ). Hint: Proceed by induction. At first I tried computing...

So if I start with a multivariate distribution f(x,y), I can find the marginal distributions, the conditional probability distributions, all conditional moments, and by the law of iterated expectations, the moments of both X and Y. It seems to me that I should be able to relate the conditional...

Hello, I've some two distributions, how can I find the distance between those two distributions? is the difference between the mean values would be the distance ?

Why distributions can not be multiplied ?? why in general can not give a meaningful expression for \delta (x) \delta ^{m} (x) or H(x) \delta (x) for example the Fourier transform (with respect to 'x') of the expression (theoretically) \int_{-\infty}^{\infty}dt (x-t)^{m}t^{n} =g(x)

can anyone help me please can anyone solve this problem for me please Q) The Binomial distribution allows the calculation of the probability of k successes in n trails where there are only two outcomes: success or fail with probabilities p and q respectively. The Binomial probability is...

Homework Statement Suppose X and Y have joint density f(x,y)=2 for 0<y<x<1. Find P(X-Y>z) According to the textbook the answer should be (1-z)^{2}/2 Homework Equations The Attempt at a Solution \int \int 2dxdy for x=[0, z+y] and y=[0,1] =\int 2(z+y) dy =2z+1 since we...

Help with simulating distributions... Homework Statement For each of the following c.d.f F, find a formula for X in terms of U, such that if U~Uniform[0,1], then X has c.d.f F. a) F(x) = 0 if 0 x<0 x if 0<=x<=1 1 if x>1 b) F(x) = 0 if 0 x<0 x^2 if 0<=x<=1 1 if x>1 c) F(x) =...

Suppose I have a result where the outcome is that with 95% confidence interval of the sample is between 27 and 42. With a second method the test result of the same sample gives a 95% confidence interval between 27 and 48. And with a third method 95% confidence interval of the sample is...

Hello everyone, I have a quick theoretical question regarding probability. If you answer, I would appreciate it if you would be as precise as possible about terminology. Here is the problem: I'm working on some physics problems that do probability in abstract spaces and the author freely...

Homework Statement suppose Fy(y)=y^3 for 0<=y<1/2 and Fy(y)=1-y^3 for 1/2<=y<=1. Compute these. 1. P(1/3<Y<3/4) 2. P(Y=1/3) 3. P(Y=1/2) Homework Equations The Attempt at a Solution Is this right for the 1. ? P(1/3<Y<3/4) P(1/3<Y<1/2) + P(1/2<=Y<3/4) (...

Homework Statement Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x^{y} (1-x)^{n-y} for y = 0, 1,..., n. Homework Equations FInd E(y) and the distribution of Y.The Attempt at a Solution f(x) = \frac{1}{b-a} = \frac{1}{1-0}...

I'm reading the first chapters of "A Guide to Distribution Theory and Fourier Transforms". On page 10, Exercises 3,6,7 the distribution is defined in terms of integrals. The first one is always without integrand (there's only the integral sign). What does that mean? Am I missing something? The...

Homework Statement The time taken by Smith to travel from A to B is a random variable which follows the normal distribution , with mean 5 minutes and standard deviation 1 minute. The time taken by Jones to travel from A to B follows the normal distribution with mean 15 minutes and SD 2...

Please teach me whether it is possible there are any distributions different from Fermi-Dirac and Bose-Einstein distributions.Because the Statistic Theorem only demontrates that integer spin particles can't obey Fermi-Dirac distribution and spin-haft particles can't obey Bose-Einstein distribution.

Homework Statement The Identity to prove: Homework Equations Using Integration by parts The Attempt at a Solution I couldn't produce the denominator.

r(x) = x if x \geq 0 and r(x) = 0 if x<0 I have to show that: 1-\[ \int_{- \infty}^{+ \infty} r(x) \varphi ''(x) dx = \varphi(0) \] And 2- that the second derivative of r is the Dirac delta. And I managed to do this by integrating by parts. Howver, I don't get why I can't just write: \[...

Homework Statement Problem description: A variable X has expected value 0.002 in meters. Consider X - 0.002, scale to millimeter, and we get Y. Tasks: a) Express Y as a function of X b) Relate the probability distributions FX and FY c) Relate the probability density functions fX and fY...

Hey guys, I'm having a bit of a problem with this question... Homework Statement If X and Y have a bivariate normal distribution with m_X=m_y=0 and \sigma_X=\sigma_Y=1, find: a) E(X|Y=1) and Var(X|Y=1) b) Pr(X+Y>0.5) Homework Equations N/A The Attempt at a Solution...

i have some values that seems to have 2 modes and i don't know how to fit a distribution to them in matlab. Does MATLAB have any function for fitting bimodal/unimodal distributions? edit: it seems like the function gmdistribution have something to do with it but this only concerns gaussian...

"Distributions" and Intergration by Parts Homework Statement Has it been proven that it is ok to use Integration by parts on "Distributions" like Dirac Delta functions inside an integration? Homework Equations Need to figure out how to write integral signs and Greek alphabet symbols...

Homework Statement A sample survey interviews an SRS of 267 college women. Suppose (as is roughly true) that 70% of all college women have been on a diet within the past 12 months. Use a Normal approximation to find the probability that 75% or more of the women in the sample have been on a...

can any Arithmetical function A(x)= \sum_{n\le x}a(n) be regarded as the train of dirac delta functions (its derivative) dA = \sum_{n=1}^{\infty}a(n)\delta (x-n) from this definition could we regard the explicit formulae for chebyshev function d\Psi(x) =1- \sum_{\rho}x^{\rho...

One of the questions in my probability homework reads: X denotes a negative binomial random variable, with p = 0.6 Find P(X ≥ 3) for a) r = 2 and b) r = 4. According to my teacher, the answers are 0.1792 and 0.45568, respectively, but I can't for the life of me figure out how he got them...

Hi guys Can one prove the identity \frac{\epsilon}{x^2 + \epsilon^2} \underset{\epsilon\to 0^+}{\to} \pi \delta(x) or is it just intuitively clear (by looking at a graph)?

Homework Statement The weight of eggs produced by a certain type of hen varies according to a distribution that is approximately normal with mean 6.5 grams and standard deviation 2 grams. What is the probability that the average of a random sample of the weights of 25 eggs will be less than...

Suppose you have multiple independent Bernoulli random variables, X_1,X_2,...,X_n, with respective probabilities of success p_1,p_2,...,p_n. So E(X_i)=p_i, and E(X_i+X_j)=E(X_i)+E(X_j). Also, \text{var}(X_i)=p\cdot (1-p), and \text{var}(X_i+X_j)=\text{var}(X_i)+\text{var}(X_j). (Though...

Homework Statement Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying...

A text file contains 1000 characters. When the file is sent by email from one machine to another, each character (independent of other characters) has probability 0.001 of being corrupted. Use a poisson random variable to estimate the probability that the file is transferred with no errors...

Homework Statement A text file contains 1000 characters. When the file is sent by email from one machine to another, each character (independent of other characters) has probability 0.001 of being corrupted. Use a poisson random variable to estimate the probability that the file is transferred...

I'm told that a product of distributions is undefined. See, http://en.wikipedia.org/wiki/Distribution_(mathematics)#Problem_of_multiplication where the Dirac delta function is considered a distribution. Now the Dirac delta function is defined such that, \[ \int_{ - \infty }^{ +...

(Note: I'm not sure about international notations or terms, but I hope everything is comprehensible) Next Monday I will pass my exam in theoretical physics about thermodynamics. However, there's still one thing that I couldn't find explicitly described in my lecture notes or any additional...

Dear Reader, I am writing for information, or a point towards any information about the calculation on the uncertainty on the number of trials in a binomial distribution. I had been using the SQRT(N) (taken from poisson dist. I miss them) but forgot they are binomial. For example if I toss a...

Hi, I wish to know if there are any naturally occurring variables that have a t-distribution or chi-distribution. I know that test statistics such as the mean or the sum of a sample has a t-distribution, where as the variance of a sample takes the chi-distribution. What I am trying to...

So I have some problems and I tried to resolve them, I also have the results so I can check them but I'm curious if I made them good. P1: (H*δ)'=?, where H is the heavisede distrobution and δ is diracs distributin. So I tried liek this : <(H*δ)',φ>=-<H*δ,φ'>=-<δ,<H,φ'>>, <H,φ'>=∫φ'dx=φ =>...

I am a Computer Science student who wants to implement the EM statistical clustering algorithm. I'm doing this on my spare time outside of any classes that I'm taking. I've been doing a lot of reading and understand almost everything I need to fully. However, I only understand univariable normal...

I read some notes answering a question about how a Z boson is made in a proton anti-proton collision and it said that the quark antiquark collision is a very rare event because the antiquark has a small parton distribution function. Surely the up anti up(or down antidown) parton distributions...

Homework Statement At a school sports day, the timekeeping group for running events consists of 1 chief judge, 1 referee and 10 timekeepers. The chief judge and the referee are chosen from 5 teachers while the 10 timekeepers are selected from 16 students. (a) How many different...

Suppose I have several exponentially distributed random variables, each of them representing the probability that some particular event occurs within some amount of time. I can't seem to come up with any intuition as to how to combine those density functions (or distribution functions) to...

Homework Statement http://photos-e.ak.fbcdn.net/hphotos-ak-snc1/hs031.snc1/2658_1060058793594_1589658877_146788_3259033_n.jpg Homework Equations The Attempt at a Solution So I know that I should use the superposition principle, and treat it as 2 superimposed spheres of opposite...

I'm currently at uni, but have difficulty doing problems involving continuous charge distributions. Say there's a charge distribution dl, dA or dV on a length surface or volume respectively at a distance R away from a point i know i must integrate over total length area or volume (depending on...

Homework Statement Let Y be the number of customers entering a ABC bank in a day. It is known that Y has a Poisson distribution with some unknown mean lambda. Suppose that 1% of the customers entering the branch in a day open a new ABC bank account. Find the mean and variance of the number of...

Hi say I have two "independent" Normal distributions, S ~ N(0,3^2) and D~(0,2^2) since I know that S and D are indpendent then P(S ) + P(D) = P(S)P(D) however we know they are both normal distributed so I amm just wondering what the general rule is for multiplying two normal...

"Pat arrives at the bus stop at some time U, which is uniformly distributed between time 0 and time 1, and waits for a bus. The first bus arrives at time T which is exponentially distributed with mean 1/μ. Assume that U and T are independent. What is the probability that Pat catches the first...