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. S

    Discrete probability distributions

    Homework Statement Here's the question: Given X is a discrete random variable. E(X-2) = 1/3 , VAR(X-2) = 20/9 . Detrmine value of E(X^2) the ans is 23/3 . but i ended up getting 3 . why i am wrong? Homework Equations The Attempt at a Solution
  2. W

    Continuous Charge Distributions

    Homework Statement A charge lies on a string that is stretched along an x-axis from x = 0 to x = 3.00 m; the charge density on the string is a uniform 9.00 nC/m. Determine the magnitude of the electric field at x = 8.00 m on the x axis. Homework Equations \int_0^3 kλ/(8-x)^2\,dx...
  3. G

    MHB Joint Probability Density from two Gaussian Distributions

    I've been reading the following paper entitled "An Improved Algorithm to Generate a Wi-Fi Fingerprint Database for Indoor Positioning": An Improved Algorithm to Generate a Wi-Fi Fingerprint Database for Indoor Positioning In Part 3.3 (Step 6), it states: Use the fingerprint database to...
  4. O

    Distributional derivative of one-parameter family of distributions

    Suppose, for a suitable class of real-valued test functions T(\mathbb{R}^n), that \{G_x\} is a one-parameter family of distributions. That is, \forall x \in \mathbb{R}^n, G_x: T(\mathbb{R}^n) \to \mathbb{R}. Now, suppose L is a linear differential operator. That is, \forall g \in...
  5. E

    For which joint distributions is a conditional expectation an additive

    I know that, for a random vector (X,Y,Z) jointly normally distributed, the conditional expectation E[X|Y=y,Z=z] is an additive function of y and z For what other distributions is this true?
  6. T

    Geometric, Exponential and Poisson Distributions - How did they arise?

    I'm going through the Degroot book on probability and statistics for the Nth time and I always have trouble 'getting it'. I guess I would feel much better if I understood how the various distribution arose to begin with rather than being presented with them in all there dryness without context...
  7. A

    Statistics and Discrete distributions

    Homework Statement The probabilities of blood types O, A, B and AB are 0.46, 0.39, 0.12, 0.03 respectively. If a clinic is seeking either type O or B from six random individuals, what is the probability that at least 2 people have the desired blood type? Homework Equations The...
  8. C

    Integrable vs. Completely Integrable Distributions

    I am a bit puzzled about the distinction between integrable, and completely integrable distributions. Before I pose my question, let me first define the terms: A distribution ##D## of dimension ##k## on ##M## is a smooth collection of ##k##-dimensional subspaces ##D_p \subset T_pM## with ##D =...
  9. A

    Combining Distributions (ex. Mixture distribution, copula)

    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...
  10. J

    Distributions within saturated solutions

    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...
  11. J

    Test functions for tempered distributions: analytic?

    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...
  12. O

    Using the Flux Formula for Different Charge Distributions

    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?
  13. carllacan

    Why are normal distributions so frequent?

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

    Stable Distributions And Limit Theorems

    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...
  15. dextercioby

    Is the space of tempered distributions 1st countable ?

    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...
  16. P

    Tractability of posterior distributions

    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...
  17. N

    Sum of independent exponential distributions with different parameters

    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) =...
  18. U

    Relationship between the Chi_squared and Gamma Distributions ?

    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...
  19. C

    Calculating Probability of Score Comparison between Two Distributions

    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...
  20. M

    Probability of at Least One 6 in 5 out of 10 Rolls of Two Fair Dice

    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...
  21. R

    MHB Applied Stochastic processes: difference of uniform distributions

    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...
  22. mesa

    Need a check on calculating prime distributions for large values

    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...
  23. C

    Comparing events in two probability distributions

    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...
  24. Astrum

    Bound Charges - Polarized Distributions

    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}...
  25. S

    Mutual Information between two Gaussian distributions

    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...
  26. P

    Calculating Probability with Normal Distribution Sample from N(μ=50, σ2=100)

    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 )...
  27. R

    Moment generating functions of continous probability distributions

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

    Approximating distributions with other distributions

    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...
  29. D

    How to calculate this probability (conditional distributions)

    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...
  30. C

    Where can I find resources to learn about distributions.

    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...
  31. E

    Variables and normal distributions

    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
  32. A

    Calculating electric fields due to continuous charge distributions

    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...
  33. S

    How Do You Calculate the PDF for Mixed Weather-Dependent Demand Distributions?

    Homework Statement demand for raincoats demand X is uniform [0,a) on a sunny day and ~U[0,b) on a rainy day. its is stated that b>a. the probability it is a sunny day is 'p' and that it is a rainy day is '1-p' (p and 1-p are constants) compute the pdf? Homework Equations f(x) =...
  34. C

    MHB Joint Probability Distributions

    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...
  35. L

    Statistics, Conditional distributions, UMVUE, Rao-Blackwell

    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...
  36. M

    Discrete probability 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...
  37. M

    Combining statistics from two distributions

    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...
  38. strangerep

    Papers by D. Carfi: extended spectral theory of distributions.

    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...
  39. E

    Uniformly charged distributions (Electricity)

    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...
  40. R

    MHB Binomial Distribution in the Exponential Family of Distributions

    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...
  41. B

    Quantify difference between discrete distributions

    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...
  42. N

    Probability, distributions

    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...
  43. W

    Exponential/Continuous Distributions

    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...
  44. W

    Statistics Continuous Distributions

    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...
  45. J

    Binomial vs Poisson Distributions

    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...
  46. Q

    (Quantum Mechanics) Gaussian Distributions, Expected Values, and Sketches

    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)...
  47. A

    Cdf of a discrete random variable and convergence of distributions

    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...
  48. N

    What is the representative fractal equation for a power law distribution?

    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...
  49. X

    Probability distributions binomial or hypergeometric

    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...
  50. M

    Modeling Public Bus Headways with Gaussian Processes

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