What is Random distribution: Definition and 13 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. A

    Break a Stick Example: Random Variables

    Hello, I would like to confirm my answers to the following random variables question. Would anyone be willing to provide feedback and see if I'm on the right track? Thank you in advance. My attempt:
  2. F

    Total movement of bacteria assuming a random distribution

    Hello, I have to find an expression for the total movement of a bacteria ##s##, knowing that the bacteria is placed (centered) on a two side ruler at position ##x=0## (so a negative ##x## value means the bacteria has moved to the left of the ruler) and that the probability it moves to ##x## is...
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    I Question pertaining to the random distribution of many worlds

    Hi everyone, I was having a conversation with my friend about the many worlds interpretation of quantum mechanics, and we couldn't figure out if many worlds implied every single last possible conceivable outcome, or if there were certain limitations that the system was confined to. For...
  4. A

    Simulating quantum coefficients

    Hi everyone, I want to generate 8 random variables (in reality to form 4 complex numbers) such that the sum of the 8 variables squared is equal to unity. The aim of generating such numbers is to perform a quantum simulation of 4 qubits (thus the 8 parameters). I've been trying to use...
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    B "Strength" of the mean of the distribution curve

    My understanding of the distribution curves is very basic but I do have a couple of somewhat generic questions. I looked up a number of definitions but have had a hard time finding these specific answers: - Is there an agreed on minimum number of samples that one needs to take to deem a result...
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    Random distribution of spheres

    Hey guys, I need to fill up a box with uniformly distributed set of non-overlapping spheres. This is quite easy to do numerically. I was wondering what is expectation value for the asymptotic volume fraction of the spheres. Suppose I have a big box with side L, and spheres with radius R<<L. I...
  7. M

    Two random distribution problems

    Basically i got to solve two problems that can be described as: if you throw 80 apples at 100 buckets randomly, and each apple must enter a bucket. How many buckets will on avarage contain 0 apple's? how many wil contain 1?, and 2?, and more? problem two: if a given number of random...
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    Numerical integration, use given random distribution as integration points

    Hi folks, I need to evaluate (numerically) a multi-dimensional integral of the form \int_A f(x) dx. Now in my application, I already have points inside the domain A which are distributed like \frac{f(x)}{\int_A f(x) dx}. So I hoped I could use these random points in some importance sampling...
  9. R

    Probability for an exponential random distribution

    Homework Statement Find the exact value of P(|Y- μ| < 1.4σ) for an exponential random variable with parameter β. Homework Equations The only equation that I can think of is the exponential distribution equation: ∫(1/β)e^(-y/β) The Attempt at a Solution I have been unable to...
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    Using stars random distribution to determine presence of gravity

    Hi, I'm sure this has been tried but I was just wondering if it's possible to use the distribution of stars and planets in the sky and see how much that deviates from true randomness. With that calculation in mind, I would then think it's possible to determine the gravitational force present...
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    Stats - Continious random distribution (PDF)

    Homework Statement A function f( x ) had the following form : f ( x) = kx^-(k+1) where 1 < x < infinity a) for what values of k is f a pdf ? Homework Equations See attachments (the theorem is included) The Attempt at a Solution started out by using the first equation in the...
  12. K

    Random Distribution of Laborers: Probability of Observed Events

    1) In a lottery there are 10 tickets numbered 1,2,3,...,10. Two nubmers are drawn for prizes. You hold tickets 1 and 2. What is the probability that you win at least one prize? Method 1: assume order matters (different order=>different outcome) P(win at least one prize) = P(win exactly one...
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    FEMLAB-Exporting Data from Random Distribution of Points?

    I am by no means an expert with FEM or FEMLAB. I am running some simple 2D axial symmetric models and would like to export displacement data for each of my subdomains. At the moment I am exporting in cooridnate & data form using a regular grid of points. However for my application the regular...