Probability distribution Definition and 203 Threads

Hi! I'm searching for guidance and help since I don't know how to solve this problem. Here it is: a) The two-dimensional random variable (ξ,η) is uniformly distributed over the square K={(x,y): 0≤x≤1 , 0≤y≤1} . Let ζ=√ξ2+η2 me the distance between the origo and the point (ξ,η) . Calculate the...

I'm watching a Stat. Mech. lecture and in it, the lecturer mentions a "general probability distribution" but doesn't explain what exactly that is, yet in the context of the video, everything necessary to understand is understood. On some cursory google searches I'm finding several hits for a...

Homework Statement We ask a person to taste 18 biscuits , 8 made to butter ( the other 10 are made to margarine ) , and to identify 8 butter cookies . He does not know the exact number of butter cookies . As he sees no difference , he randomly selects those he claims to be butter . Y = the...

Homework Statement The joint probability density function of X and Y is given by f(x,y)=(6/7)(x^2+ xy/2) , 0<x<1, 0<y<2. (a) Find the pdf of X. (b) Find the cdf of X. (c) FindP(X<.5). (d) Determine the conditional pdf of Y given X = x. The Attempt at a Solution a) the pdf is what is...

Homework Statement 4. Let X and Y have the joint probability distribution (a) Find P(X +Y ≤ 4). (b) Find the marginal probability distributions f1(x) and f2(y). (c) Find P(X < 2|Y = 2). (d) Are X and Y independent? The Attempt at a Solution a) f(1,1) + f(1,2) + f(1,3) + f(2,1) + f(2,2) +...

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the...

Homework Statement 1. Consider selecting at random a student who is among the 15,000 registered for the current semester at a school Let X be the number of courses for which the selected student is registered and suppose that X has probability distribution x: 1 2 3 4 5 6...

Homework Statement An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year. a). How many loads can be expected to occur during a 4-year period? b). What is the probability...

hello all.glad to be here! please in the attached document, column 5 and 6 which represents the differential and cumulative frequency distributions were obtained using equations (5) and (6). I'll be mighty grateful if anyone can give me a step by step breakdown of how it was done?? Many thanks...

Hello, I am analysing hydrology data and curve fitting to check the best probability distribution among 8 candidate distribution. (2 and 3 parameter distributions) The selection is based on the lowest AIC value. While doing my calculation in excel, how is it suggested to treat very low (approx...

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...

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...

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 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...

Can someone explain why the probability of the inclination angle of a binary system being less than i_0 is 1-cos(i_0) i.e. why the fractional distribution of binary stars is df = sini * di, where i is the inclination angle? Where does the sin i come from? Why is not not uniformly distributed...

"In multivariate probability distribution higher-order cumulants contain information of decreasing significance, unlike higher-order moments".

According to wiki: http://en.wikipedia.org/wiki/Poisson_process The probability for the waiting time to observe first arrival in a Poisson process P(T1>t)=exp(-lambda*t) But what is the Probability Distribution P(T1=t) of the waiting time itself? How to calculate that?

I am studying an article which involves stochastic variables http://www.rmki.kfki.hu/~diosi/prints/1985pla112p288.pdf. The author defines a probability distribution of a stochastic potential V by a generator functional G[h] = \left<exp\left(i\int...

Homework Statement I have a question that looks so stupid that I have never dared to ask. If I want to measure the time average from t=0s to t=1s of a given f(t), the solution is compute the following integral: TA = 1/T*∫F(t)dt However, I have some doubts about this calculus.Homework...

Homework Statement http://postimg.org/image/bleosmrep/ Homework Equations The Attempt at a Solution can someone explain the last line of the solution; where did 1 - 6.25/10^2 come from?

Hi! Suppose we have two variables Y and Z that depend on a third one, X. We are given P(x), P(y|x) and P(z|x). The joint probability distribution P(x,y,z), according to the chain probability rule, is given by P(x,y,z) = P(x)P(y|x)P(z|x,y) But how can we compute P(z|x,y) with the given...

Homework Statement The ground sate of a Hydrogen-like atom is given by the wavefunction: $$R_{10}(r)= 2\left(\frac{Z}{r_0}\right)^{3/2}e^{Zr/r_0}$$ and the Probability distribution is $$P(r)=4\pi r^2 |R_{10}|^2$$ At what distance is the most probable radius of the electron? Homework...

A problem i made up for some of my friends who need help with discrete distributions tables. Can you do it? Dice Generator Part I: 1. Construct a discrete probability distribution table for a fair six-sided dice. (Round according to example) 2. Calculate the mean, variance, and standard...

The number of hours, N, of daylight at a certain location can be expressed as N(d)=12+6sin(2πd/365) where d=day of the year starting with March 21. (a) What is the probability distribution function for hours of daylight if you assume the day of the year is a random variable? (b) What is the...

A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next...

I have found that: For l = 1: \sum_{m=-l}^l |Y_l^m|^2 = \frac{3}{4\pi} For l = 2: \sum_{m=-l}^l |Y_l^m|^2 = \frac{5}{4\pi} What significance does this have for the probability distribution in an hydrogen atom?

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...

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...

f(x)=f(x)={█(2/(√2π) e^(〖-x〗^2/2)@0 otherwise)┤for 0<x<∞ Find the mean and variance of X The hint says, compute E(X) directly and then compute E(X2) by comparing that integral with the integral representing the variance of a variable that is N (0, 1)

Hello, The following problem can be found in van Kampen's "Stochastic Processes in Physics and Chemistry", Third Edition (Exercise I.3.7): The probability distribution of lifetimes in a population is P(t). Show that the conditional probability for individuals of age τ is...

Hi, I'm comparing different measurement methods. I listed and derived an equation for each error component per measurement method and calculated the probability distribution using the Monte-Carlo method (calculating each error 300.000 times assuming a normal distribution of the input...

Homework Statement f(x,y) = x2 + xy3 for 0 < x < 1, 0 < y < 2 and 0 otherwise. Calculate P(X+Y < 1) Homework Equations The Attempt at a Solution P(X+Y < 1) = P(X < 1-Y) which means y is now bounded by 0:1 instead of 0:2 and x is bounded by 0:y. So we get ∫[0-1]∫[0-y] x2 +...

Homework Statement Consider a Hamiltonian involving two Gaussian variables, X and Y. Start from the statement that the average formed by these two variables is of the form <e^{aX+bY}> = e^{a^2+b^2-ab} Homework Equations <e^{ax}> = \int_{-\infty}^{\infty} dx \frac{exp(-\beta (...

Hey everyone, This is my first time posting on PF! I want to model the photons ejected from a blackbody source at temperature T. The question I want answered is: given a photon is detected, what is the probability of the photon having a wavelength λ? This amounts to just attaining the...

Homework Statement $$P_x(x)=A(1- \frac{|x|}{2}) \ \ \ |x|≤2$$ $$P_x(x)=0 \ \ |x|>2$$ Find A Homework Equations The Attempt at a Solution This one shouldn't be too bad but I wanted to verify that I am on the right track. I basically have ##P_x(x)=A(1- \frac{x}{2})## when x≤2. 0 otherwise...

Homework Statement Suppose that x measures the time (in hours) it takes for students to complete an exam. All students are done within 2 hours and the density function for x is given by f(x)={(x^3)/4 0<x<2 {0 otherwise Compute the median of this distribution. (Give an exact...

Homework Statement f(x) = C|x-2| for 0 <= x <= 3 f(x) = 0 otherwise Homework Equations The Attempt at a Solution Solved for C, found it to be (2/5). So.. I'm confused how to set up my integral here. I tried integral(2/3(x-2)dx) from m to 3 = 1/2. That didn't yield the correct...

Homework Statement Uploaded Homework Equations Uploaded The Attempt at a Solution Is my work correct?

Homework Statement The question is "Comment on the physical consequence of two probability distributions being equal to each other even though the probability amplitudes are not the same." Homework Equations The Attempt at a Solution I understand that the modulus squared of the...

Differences between binomial distribution and "forced" probability distribution Hi everyone. Yesterday I was thinking about probability and real life and about the fact that we always expect life's facts to behave according to probability theory. If we flip a coin and we get 6 times heads...

According the the kinetic theory of gases, molecules moving along the x direction are given by Σx= (1/2) mv^2, where m = mass and vx is the velocity in the x direction The distribution of particles over velocities is given by the Boltzmann law p(x)=e^[(-mv^2)/ekT] where velocities range from...

Sometimes it is said that the probability distribution which does not add up to 1 still can be used to find relative probabilities. For example, consider probability distribution p_n = 1/n for all natural numbers. Does it make sense to say n = 1 is twice as probable as n=2, even if total...

I'm completely lost on this probability problem, Homework Statement A Box contains 5 indiscernible CDs.It is known that among them 2 are for children .So in order to find the first children's CD ,they are tested one after the other (successively ),Denote by X the random variable which...

The distance of someone from the center (cable station) of a circle is depicted as r, and the regular radius of that circle(the cable station) is depicted as rc. The Circle represents the entire area the cable station provides cable service for. Given: Probability Distribution Function P(r) =...

I was browsing the 1998 STEP paper 3 (like you do) and come across a question related to a real intelligence gathering problem. It has some simplifications and probably invalid assumptions, but is still quite interesting. The question is: I don't intend to solve this since the only question...

Hello Everybody. I have a rather simple question, which still kept me thinking for two hours without any result. If we want to determine the multiplicity in the microcanonical ensemble we just divide the volume of the shell containing the accessible microstates over the volume of one...

Homework Statement Consider the experiment of tossing a fair coin 4 times. What is the probability distribution of the number X of heads? The Attempt at a Solution I got (0.5)(0.5)(0.5)(0.5) = 0.0625 but its wrong and I don't know why

Homework Statement Incoming signal has normal distribution, xmin is equal to -sigma, xman is equal to +sigma. What is the governing equation of the nonlinearity through which the signal has to be passed in order to make its pdf uniform? Homework Equations...

Suppose two teams play a series of games, each producing a winner and a loser, until one team has won two more games than the other. Let Y be the total number of games played. Assume each team has a chance of 0.5 to win each game, independent of results of the previous games. Find the...

This is hopefully a simple question... Given the first n moments or central moments or cumulants (I don't care which) of a probability distribution, is there a standard procedure for estimating its functional form? For example, I know that given the mean and variance of a distribution...