Gaussian distribution Definition and 67 Threads

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.

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...

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...

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...

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...

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?)

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.

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...

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...

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...

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...

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...

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...

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!

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...

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

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