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. P

    IQ scores and normal distributions

    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...
  2. D

    Probability Distributions

    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...
  3. S

    Exploring Integration: A Guide to Probability Distributions

    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...
  4. N

    Statistics Help Requested (Discrete Distributions)

    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...
  5. B

    Deriving probability distributions

    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...
  6. J

    Ratio of 2 Gamma distributions

    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?
  7. E

    What is the estimated number of animals in a forest using a Poisson model?

    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...
  8. E

    Distributions with Infinite Mean: Examples & Possibilities

    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!
  9. K

    Probability : joint density function of 3 Normal Distributions

    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 ?
  10. O

    Joint and conditional distributions

    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...
  11. M

    Calculating Sum of Three Correlated Gaussian Distributions

    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...
  12. RogerPink

    Heisenberg Uncertainty Principle and Gaussian Distributions

    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...
  13. D

    What is the probability of merging two poisson processes?

    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...
  14. E

    Why can,t we multiply two distributions?

    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...
  15. R

    Max amount of different bridge distributions?

    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?
  16. S

    Pdf of the sum of two distributions

    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...
  17. S

    How do you know which distribution to use for your problem?

    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
  18. W

    Understanding Standard Deviation for Sample Means in Statistics

    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...
  19. maverick280857

    Gaussean Surfaces [Can they pass through charge distributions?]

    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...
  20. A

    Newtonian Probability Distributions

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

    What Are Good Resources for Understanding Basic Probability Distributions?

    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...
  22. DaTario

    Nice derivations of Maxwell, Fermi-Dirac and Bose-Einstein distributions

    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...
  23. W

    How to Estimate the Intrinsic Distribution

    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...
  24. M

    Need help with statistics / distributions

    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...
  25. F

    Identifying distributions in time series

    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
  26. Z

    Fourier analysis and prob. distributions?

    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...
  27. H

    Computing Statistical Distributions: A Practical Guide

    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.
  28. homology

    Charge distributions & delta functions

    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...
  29. M

    Solve for a with P(0 < z < a)=0.2 | Math Help

    How would I solve for a on a question like this: P(0 < z < a)=0.2 ? I know that for a question like P(z < a)= 0.85 I would find the inverse-norm of 0.85 to solve for a. I've tried the same thing for the first question, but of course it doesn't work and I'm out of ideas as to how else I should...
  30. M

    How do I determine the area within 0.5 standard deviations of a given z-value?

    Could someone please tell my how I would determine the area within 0.5 standard deviations of a given z-value? The first one is z=0. What do I need to do?
  31. F

    Statistical Probability Distributions

    I have two questions, I've completed. I am partially sure that the answers I've obtained are correct, and all I really want is confirmation on whether they are correct or not. If not, what am I doing wrong? Question 1: If the joint probability distribution of X1 and X2 is given by...
  32. C

    What Are the Limitations of Multiplying Delta Functions in Quantum Mechanics?

    Hi, I am not seeking a "complete" treatment of distribution functions (like Gelfand or Schwartz). However, I would like some discussion in regards to multiplying delta functions together---especially in QM. From the little I have discovered, distributions do not form an algebra, and thus...
  33. K

    What are Some Questions on Probability Distributions?

    hey guys.. Im having trouble answering the following questions I tried everything I can. I JUSS don't get it 1)In a common carnival game the player tosses a penny from a distance of about 5 feet onto a table ruled in 1-inch squares. If the penny (3/4 inch in diameter) falls entirely...
  34. A

    Statistics Problem: Sampling Distributions - Somewhat OT

    You are on the staff at the Post Office. Your job is to find a process to find the average waiting time for service. How do you collect the data, and once it is collected, what do you do next?
  35. humanino

    Generalized parton distributions

    In some of my previous posts, I referred to GPDs, a recently developped formalism describing hadronic states. I am afraid that this formalism remains largely ignored partly because few introduction review are only recently available. See for instance : Markus Diehl, Phys.Rept. 388 (2003)...
  36. J

    Generating Function for Probability of Equal Sums in Multinomial Distributions?

    I don't understand the generating function used to find the probability that the sum of the numbers of occurring events is a certain quantity. Specifically, I'm having trouble with this problem: "Find the probability of purchasing a ticket with a number whose sums of the first three and last...
  37. I

    Calculating Mean Probability with Sampling Distributions | Sample Size 200

    The mean probability of 100 observations is .0422. If you are not given the data for a sample size of 200, how do you find the mean probability of this data using the mean probability you found from .0422? thanks
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