# gaussian

1. ### Gaussian distribution and Likelihood

i have question regarding the plotting the expression of gaussian distribution and likelihood see attachment Thanks
2. ### Gaussian Elimination problem.

12x-4y=20 2y-6x=-10 I did the Gaussian method, and I got 1 0 = 5/3 which means x= 5/3, and I also got on row 2, y=0. However, the answer is : x=y/3+5/3. Where did they get the y/3??
3. ### Gaussian Elimination

For the following, find (if possible) conditions on a, b and c such that the system has no solution, one solution, or infinite many solutions. x + ay - z = 1 x + (a - 2)y + z = 1 2x + 2y + (a - 2)z = c
4. ### Gaussian Elimination reduced to row Echelon form.

First time posting, sorry if I'm in the wrong topic. Can anyone explain how to do this question? Any help is appreciated.
5. ### Newton's method - Gaussian Elimination

Hi, I don't fully understand the use of Guassian Elimination in Newton's method.. What does it do and how does it help us?
6. ### operation count for Gaussian Elimination

I know additional line of finding a new pivot and swapping doesn't change the operation count , of gaussian elimination, can someone please explain why this is the case?
7. ### Gaussian elimination

Can someone please explain something to me, when performing guss elimination why is it that the system A *x = b is equivalent to the two other systems L*y = b U*x = y I know A = LU, but why is equation 1 equal to the other two. ?
8. ### Gaussian elimination

I have this system to solve $x+y+z=4 \\ z=2 \\ (a^2-4)z = a-4$ and I gotta find the values for a such that it has no solutions, one solution, infinite solutions 1) $a^2-4 \neq 0$ I get $\left[\begin{array}{cc}1&1&0 : 2 \\ 0&0&1 : 2 \\ 0&0&0:\frac{1}{a+2}-2\end{array}\right]$ if I solve...
9. ### Estimate paramters of gaussian likelihood and gaussian prior from posterior sample?

Hi, I have a bunch of 2D data which I want to interpret as samples from 11 different posterior (gaussian) distributions. I can obviously estimate the covariance and mean of these posteriors from the data, but what I really want to do is estimate the parameters of the underlying (gaussian)...
10. ### Copula Calculation

I have the following question I need to answer. Suppose X1 and X2 are two standard normals and are joint normal with correlation ρ. Compute the Gaussian copula function C(u1, u2) for (X1, X2) with the following value of ρ ρ = 0 ρ = 1 ρ = 0.5 (In this case, the copula function has no...
11. ### Gaussian Method

I want to know the row operations to solve this question. 2 x-7y+4 z=9 x+9y-6z=1 -3x+8y+5z=1 First row operation i used is 2*R2-R1 then i used 3*R2+R3 but now i m dont know what to do to.
12. ### Solution set for Ax = 0 and Ax = b with Gaussian Elimination + General questions

General Question: Currently we are working with the Gaussian Elimination and I have some questions about the resulting matrixes. Matrix 1: When my last row looks like in the picture, what does it tell me about the matrix and the result? What are the properties of such a matrix where I have no...
13. ### How to integrate double exponential and gaussian?

Hi, I encountered this integration, where the integrand is the multiplication of double exponential and a gaussion... \int^{\infty}_{0}e^{-x^2}e^{e^{-x}}dx. By doing the change of variable y=e^{-x} seems not to do the job... Anyone knows how to integrate it? Thanks a lot!!
14. ### Exact inversion of matrix complexity (by Gaussian elimination)

I would like to check if what I have done is correct. Please, any input is appreciated. **Problem statement:** Consider a non-singular matrix $A_{nxn}$. Construct an algorithm using Gaussian elimination to find $A^{-1}$. Provide the operation counts for this algorithm. **My attempted...
15. ### Gaussian Norms

1. The problem statement, all variables and given/known data Suppose p is a prime number. Prove that p is irreducible in Z[√−5] if and only if there does not exist α ∈ Z[√−5] such that N(α) = p. Using this, find the smallest prime number that is not irreducible in Z[√−5]. 2. Relevant equations...
16. ### Gaussian Elimination (Systems of Equations) Word Problem

[vendors] sell an herbal tea blend. By weight, Type I herbal tea is 30% peppermint, 40% rose hips and 30% chamomile, Type II has percents 40%, 20% and 40%, respectively, and Type III has percents 35%, 30% and 35%, respectively. How much of each Type of tea is needed to make 2 pounds of a new...
17. ### Gaussian Elimination Help!

Hi guys, I've been given a question that asks me to use Gaussian elimination to reduce the following system of equation to row echelon form, hence solving for x, y, z and w x+2y+z+w=1 2x+y-z-w=2 x+2y-3z+w=-3 x-y+z-w=3 I'm not really too comfortable with Gaussian elimination but so far I've...
18. ### Fitting a Gaussian to high dimensional data with a discrete pdf defined over them

Hi, I wonder if anyone can give me a handle on this problem. I have sampled 100,000 point from an isometric gaussian in 98 dimensional space (each point translates into a particular face in a "face space" model). I have then defined a uniform distribution over the 100, 000 points. so far so...
19. ### gaussian and linear indep

Hello smart people, I am having some concept difficulty. This is what I dont understand...... Determine the column space of A(see image above) Use Gaussian elimination to check whether or not an arbitrary vector x Please see the following picture insert. corresponds to a plane in R^3.Any basis...
20. ### unknown Gaussian surfaces?

wrinkled sphere Gaussian surface? I invented this problem you don't have to do it, take 2 wrinkled spheres of opposite charge rhocharge2 and equal radius, volumerho1 of the spheres=1+\frac{1}{2}sin(m\pi) sin(n\phi), m=6, n=5 the spheres overlap in a region and the vector between the centers...