Gaussian distribution Definition and 73 Threads

  1. A

    Show that a Gaussian Distribution Corresponds to a CTS random variable.

    Going over my Lecture Notes my Lecturer as Started with Show that a Gaussian Distribution Corresponds to a CTS random variable. Then she has i) Taken the f(x) = [p.d.f] and shown a) f(x) >= 0 for all x member of real numbers. b) Integral over all real numbers = 1 ii) Found the M.G.F then...
  2. V

    What is the basic difference between Maxwell and Gaussian Distribution?

    Can anyone tell me the basic difference between Maxwell and Gaussian distribution? Thanks in Advance
  3. X

    Gaussian Distribution Question.

    I am studying the Gaussian distribution and am doing one of the problems for practice. The problem states that the standard deviation is equal to 15 and the actual value recorded in the experiment is 385.0. It then asks what is the probability that a single measurement lies in the range of the...
  4. M

    Sampling of a gaussian distribution

    I have a 3d data cube. For every point I measure the property A which is a gaussian variable of mean m and variance s and it's also a function of the density d at every point. A(x,y,z)=f(d(x,y,z))e^(-(X-m)^2/(2\sigma^2)) X is a random number. Now let's say I want to sample the...
  5. S

    Raw moments of Gaussian Distribution

    I'm wondering if there was a table of moments for a Gaussian Distribution, I found one up to the fourth moment U \sim N(\mu, \sigma^2) E[U^2]=\mu^2+\sigma^2 E[U^3]=\mu^3+3\mu\sigma^2 E[U^4]=\mu^4+6\mu\sigma^2+3\sigma^4 I'm doing a problem right now and i need the 8th moment.
  6. D

    Calculating percentile ranks of a Gaussian distribution

    I have been calibrating a sub-micron particle sizer with 1 um (1000 nm) standard. After testing the standard, the test results on my print-out: (X25 = 812.7 nm, X50 = 977.7 nm, X90 = 1389.0 nm) According to USP, the limits are +/- 6% of the reference standard values for X25, X50, and X90...
  7. E

    What Is the PDF of a Circularly Symmetric Complex Gaussian Vector?

    Hi, Suppose that an n-dimensional vector \mathbf{z}=\begin{pmatrix}z_1&z_2&\cdots & z_n\end{pmatrix}^T is characterized as a zero-mean circularly symmetric complex Gaussian random vector. What is the distribution (the probability distribution function PDF) of this vector in both: complex and...
  8. W

    Statistical Error of Centroid of Gaussian Distribution

    Statistical "Error" of Centroid of Gaussian Distribution If I have L data samples, distributed randomly (3D real Gaussian distibution, unity variance) about the origin in 3D real space, how can I derive an expression for the "origin estimation error" (i.e. the distance between the true origin...
  9. D

    1 Dimensional Representation of a Gaussian Distribution

    Hi, I currently have a Gaussian distribution (Normalized Frequency on the y-axis and a value we can just call x on the x-axis). So for the sake of simplicity, let's say that I ignore any values below 0 and any values above 1 on the x-axis. Then what I will do is take 10 equal segments...
  10. D

    How to Represent a Gaussian Distribution in 1D?

    Hi, I currently have a Gaussian distribution (Normalized Frequency on the y-axis and a value we can just call x on the x-axis). So for the sake of simplicity, let's say that I ignore any values below 0 and any values above 1 on the x-axis. Then what I will do is take 10 equal segments...
  11. A

    Calculate Expectation Value & SD of N1, N2 in 0.1m^3 Vacuum Chambers

    The conc.of molecules in two ultra-high-vacuum chambers of volumes V1=V2=0.1m^3 is 10^6 molecules/m3 You count the # of molecules N1 and N2, in each chamber at some moment of time. a.find the expectation value and the SD of N1 and N2 . calc \sigma_{N1}, sketch the prob distribution of N1...
  12. H

    Intersection of two gaussian distribution functions

    Can you please give me formulas which give intersection of two gaussian function f(x, mu, sigma) = 1/sqrt(2*pi*sigma^2) * exp(-(x-mu)^2 / (2*sigma^2)) for the case variances are different. (Note: I think it is time I learn how to use "tex" tags, do you know a good tutorial?)
  13. R

    What are the variables at the center of a Gaussian distribution problem?

    Q. (Something), (Something) and (Something) is at the centre of distribution.(bell curve) The mean? And i don't know - I've read through my maths book(s) and several other sources of information and can not find any information. Thanks.
  14. P

    Question about Gaussian distribution

    Hello everyone, I am trying to understand situations under which Gaussian distribution would apply. For example, I read somewhere that if you have some ink drop on a porous paper, then the distribution of the displacement of ink particles is approximately gaussian. I am trying to figure...
  15. D

    How to solve an integral of a gaussian distribution

    Homework Statement integrate \int_{-\infty}^\infty\! e ^{(x-a)^{2}}\, dx Homework Equations \int \! e^u\, du = e^u + C The Attempt at a Solution i just know that du = 2(x-a), but there is no x to make use of substitution, so I am confused on how to go about solving this since I...
  16. M

    Chi Square Test for Gaussian Distribution

    Hi there, I have very naive to statistics. I have a set of data points. that can be like 10, 12, 13, 14 ,15 , 15, 12, 13 17, 18, 19, 12, 19, 20 .... Now i need to know if these days points follows any gaussian distribution / normal distribution or not? IS chi -square test the right...
  17. D

    Derivation of Gaussian Distribution

    Homework Statement Derive the equation for the Gaussian distribution. Homework Equations The probability density function for the Gaussian distribution: f(x) = \frac{1}{\sigma \sqrt{2\pi} } e^{ -\frac{(x-\mu)^2}{2\sigma ^2} } The Attempt at a Solution It is my understanding that the...
  18. D

    Solving Gaussian Distribution Problem: Find (Δx)^2 and Uncertainty δp

    Problem Let us define a wave function \phi = A \exp \(\frac{-(x-x_0)^2}{4a^2}\) \exp \(\frac{i p_0 x}{\hbar}\) \exp(-i \omega_0 t). Show that (\Delta x)^2 = a^2. Also, calculate the uncertainty \delta p for a particle in the given state. Attempt at a solution I honestly have no idea as to...
  19. B

    MATLAB Please help me with Gaussian Distribution and central limit theorem in matlab

    please help me with Gaussian Distribution and central limit theorem in matlab! :cry:I am trying to generate a random variable with a approximate gaussian distribution using the rand function and central limit theorem, got stuck when trying it. Please help me. Also want to know how to produce a...
  20. H

    Solve Physics Problem: Gaussian Distribution

    Hello, I am attaching what was an extra credit question in my physics class which I didn't understand at all. The topic isn't in the book and all the internet searchs I read confuse me. I was hoping someone might give me a walk through. Thanks!
  21. L

    Is a gaussian distribution 'like a sine wave'

    So I was having a conversation with the guy I share an office with and I brought up the gaussian distribution to show the probability distribution of energies of electrons generated by a filament. He mentioned that it 'looks like a sine wave', and I said 'sorta, but it's not a sine wave'. He...
  22. R

    Sets of numbers and Gaussian distribution

    Are there any sets of numbers that represent numbers of sets? Any sets of numbers that follow a Gaussian (normal) distribution?
  23. D

    What are some helpful math websites for understanding the Gaussian distribution?

    Hi i need a good math site (easy to read) so i can find the gaussian distribution
Back
Top