What is Distributions: Definition and 337 Discussions

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). Examples of random phenomena include the weather condition in a future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc.

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  1. M

    Help with negative binomial distributions

    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...
  2. N

    Limit of Lorentz distributions

    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)?
  3. L

    Probability Question - Nonstandard Normal Distributions

    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...
  4. S

    Skewness and Kurtosis of Bernoulli Distributions

    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...
  5. E

    Discrete Random Variables and Probability Distributions

    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...
  6. K

    Poisson and binomial distributions, corrupted characters in a file

    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...
  7. K

    Probability - random variables, poisson/binomial distributions

    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...
  8. F

    Product of dirac delta distributions

    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 }^{ +...
  9. C

    What exactly determines a bivariate distribution in statistics?

    I'm having some trouble wrapping my head around multi-variate distributions. Most textbooks describe it by starting off with two random variables X, Y and introducing P(X \leq x, Y \leq y). This initially led me to believe that X, Y uniquely determine the distribution over R^2 - I later...
  10. R

    Show convergence of product of n uniform distributions

    Homework Statement Suppose X_1, X_2, \ldots X_n are iid random variable each distributed U[1,0] (uniform distribution) Suppose 0 < a < b <: Show that: P((X_1X_2 \ldots \X_n)^{\frac{1}{\sqrt{n}}} \in [a,b]) tends to a limit as n tends to infinty and find an expression for it Homework...
  11. P

    The average and variance of distributions (thermodynamics)

    (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...
  12. C

    Mixed Distributions Homework: Showing Marginal Distribution of X

    Homework Statement Let X ~ Poission (\lambda \theta). Suppose \lambda ~ gamma (h,h-1) and \theta ~ generalized Pareto (\alpha, h-1,k). Show that the marginal distribution of X is \frac{\Gamma(\alpha + k) \Gamma(\alpha + h) \Gamma(\alpha + x) \Gamma(k + x)}{\Gamma(\alpha) \Gamma(h)...
  13. P

    Uncertainty on the number of trials in binomial distributions?

    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...
  14. M

    Variables with t and Chi-sq distributions

    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...
  15. D

    Distributions: Convolution product

    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 =>...
  16. X

    Layperson's description of multivariate gaussian distributions?

    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...
  17. P

    Parton Distributions in PP collisions

    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...
  18. C

    Solving Probability Problems with Discrete 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...
  19. G

    Combining exponential distributions

    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...
  20. P

    Superposition of Spherical Charge Distributions

    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...
  21. S

    Electric field's due to continuous charge distributions

    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...
  22. K

    Multivariate probability distributions?

    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...
  23. C

    Multiplying Normal Distributions: Rules & Examples

    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...
  24. T

    Solving Two Distributions Probability Question

    Homework Statement "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...
  25. T

    Problems involving two distributions

    "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...
  26. S

    Random number generator of 2 normal distributions partially correlated

    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.
  27. P

    'Triangular Distributions' Probability Density Function

    (\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...
  28. G

    How to determine if distributions are correlated?

    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...
  29. J

    Distributions and delta function

    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 ...
  30. D

    Electric field of charge distributions

    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)...
  31. C

    Combining Distributions for Accurate Function Timing: A Statistical Approach

    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 are of no...
  32. S

    Combinations and probability distributions

    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...
  33. D

    Charge distributions vs. voltage on an infinite plate

    Don't know if this is the right place to post it, but oh well:rofl: 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...
  34. E

    Normal and power law distributions

    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...
  35. J

    Dalitz plots & mass distributions

    Homework Statement We are given a reaction X_{1} + X_{2} \rightarrow Y_{1} + Y_{2} + Y_{3}. The quantities m_{Y_{1}Y_{2}}^2 and m_{Y_{2}Y_{3}}^2 are plotted in a Dalitz plot. Y_{1} + Y_{2} resonate at a fixed mass m_{Y_{1}Y_{2}}. Show how this resonance leads to a mass distribution for...
  36. S

    Potentials from continuous distributions.

    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...
  37. N

    Solving for Charge & Current Distributions

    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...
  38. MathematicalPhysicist

    Computing distributions by using convolution.

    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...
  39. Somefantastik

    Probability Distributions

    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?
  40. G

    One sided testing of two Poisson distributions?

    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...
  41. MathematicalPhysicist

    What is a Marginal Distribution and How Does it Apply to F1(x)F2(y)?

    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...
  42. W

    Arrival,wait and service distributions

    [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...
  43. S

    Binomial and geometric distributions

    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)...
  44. J

    Non-integrable tangent distributions

    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.
  45. D

    Transforming angular distributions between different reference frames

    My problem is related to the Brookhaven experiment of the J/psi discovery and the Y discovery at Fermilab (in both cases, protons over a Berillium fixed target). In both cases they had a resonance decaying into two leptons, and the detecting system consisted of two arms, covering a relatively...
  46. K

    Normal vs. LaPlace Distributions: Critical Values

    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...
  47. B

    Pressure distributions around solid objects

    Homework Statement What is the p_\infty term that arises in many expressions for pressure distributions around solid objects? Homework Equations An example is p = p_\infty - \frac{7}{2}\cos \theta The Attempt at a Solution I've seen the p_\infty come up very often in...
  48. N

    Advice on Exponential, Binomial, & Normal Distributions

    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...
  49. E

    Energy eigenvalues and momentum distributions

    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...
  50. K

    Fourier transform of distributions.

    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...
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