1. M

    How do I find the mean of Z = Discrete RV + a Gaussian RV?

    Hello, I am asked to find mean and variance of Z. (image in attachment) Since I am solving a preparatory examen to study, it is not clear to me how to approach the topic because I don't understand the question correctly. What are the steps to follow given the nature of the RV "Z" ...
  2. L

    Using the result of the Gaussian Integral to evaluate other funky integrals

    I evaluated the Gaussian integral using polar substitution, and got an answer of sqrt pi But my professor also asked us to compute the integral e^(-x^2/2) from negative to positive infinity and the integral of x^2(e^x^2) from 0 to infinity. ... and using our results from the previous step...
  3. J

    Conditional distribution of X given Y when both X and Y are gaussian

    Two Random variables X and Y are gaussian.Is the conditional distribution of X given Y that is X|Y also a gaussian when Y lies in certain range from a<=y<=b?I know its true when y has a specific value but what if it lies in a certain range as mentioned above?
  4. L

    Gaussian integers

    Pick up prime elements of the ring of Gaussian integers G = {a+ib/a,b \in R} from the following: A) 2 B) 3 C) 7 D) 13 My answers : Options B & C please check and let me know... Thanks. :)
  5. E

    Function Approximation as Multivariate Gaussian

    Is there any existing method to approximate a (multivariate) function at an arbitrary point as a multivariate gaussian to get a gaussian that fits the function best close to that point, by only evaluating the function (and possibly calculating the Hessian) at the point of interest?
  6. H

    inverse gaussian distribution

    hi, for X~IG(m,l), IG:inverse gaussian, the characteristic function C_X(t)=E[exp(itX)]=exp{m/l (1-(1-2im^2 t/l)^1/2)} i need help to demonstrate that: and differentiating C_X(t) by r times and letting t=0 E[X^r]=m^r \sum_{k=0}^{r-1}(r-1+k)!/(k!(r-1-k)!)(m/2l)^k
  7. Z

    Gaussian Elimination Using Scaled Pivoting

    when we create the initial matrix s for the largest values in each row, do we switch the values in the matrix s when we switch rows or keep them as they are?
  8. E

    Max-Marginalisation of Conditional Gaussian Distributions

    I need a way of approximating the result of performing a max-marginalisation operation on a conditional gaussian (that is a function of both discrete and continuous (gaussian) variables) as a gaussian mixture. I can't seem to find any methods for doing this in the literature.
  9. E

    Approximating Quotient of 2 Gaussian Mixtures as single Gaussian Mixture

    I need a way of approximating the quotient of 2 gaussian mixtures (i.e (N1+N2+N3)/(N4+N5+N6)) as a single mixture (i.e N7 + N8 + N9)
  10. C

    Gaussian Elimination

    I've attempted this problem and got that it has infinite solutions. In the first instance, are the row reductions I've done valid and correct? And if so, how do I get solutions from the last bit? Any assistance appreciated. Thank you.
  11. M

    gaussian distribution and integral

    the first factor is a gaussian distribution but I didn't get it how the integral was calculated? Is there any theorem in this case thanks --- I got that sorry for this question
  12. H

    Gaussian Variables

    Hi, I have a problem to dertermine Ry1y2 (autocorrelation) from an exercice, here is the statement: X1 and X2, jointly gaussian variables characterized by (mx)=(1, -2); (Cx)= "as a matrix"(9 -3)1st line (-3 4) 2nd line of the matrix are subjected to the linear transformation Y=AX where A=(1...
  13. H

    Convolution of two Multivariate Gaussian PDFs

    I am looking for a proof for convolution of two multivariate Gaussians (where each Gaussian has multi-dimensional mean and co-variance). I found a proof in here: where it provides a proof for convolution of two uni-variate Gaussians and also it...
  14. A

    Standard Deviation of Squared Gaussian Distribution

    Hello Everyone, I have a quick question. Assuming we have a random variable described by a Gaussian probability density function: f(x) = 1/((2*pi)^0.5*s)*exp(x^2/(2s^2)) If a new random variable is defined as: y = x*x. What would be a probability density function describing it and what...
  15. F

    energy of a electrical impulse

    Hi, I have an APD (Avalanche Photo Diode) to detect light (amount of photons) in form of an impuls. The output of this APD is a gaussian function, see attached picture. As you see there, we have two parameters...Amplitude (A): 0.9 Volt and the Full With at Half Maximum (FWHM) of 10...
  16. J

    Gaussian Elimination Type Method Needed

    Hi, I'm struggling a bit with the following problem: 3 + 14*x = 1 + 25*y = 9 + 288*z I have a series of these equations which I need to solve, with different first terms in each case and one of these first terms changes for each equation: e.g. the second such equation is: 3 + 14*x = 1 +...
  17. Maurux

    Calculate det(a) using Gaussian Method

    I don't understand how to get 33 as det of A |2 3 -2 4| |2 4 -3 2| |1 3 2 1| |0 1 2 3| I tried to swap row 3&4 to 1&2 and get my echelon lower bound triangles for I get det(A)= 1 I tried without swaping, step by step zero each rowxcolumn but I end up with det(a)= 22 Could...
  18. E

    Probability density function of a band limited signal / noise

    Hey guys, can anyone tell me, how frequency depends on a gaussian distributed signal? Background is following: I have a normal distributed noise (or signal), that is not band limited ( -> over the complete spectrum!) with the probability density function (pdf) : p_G(z) =...
  19. T

    Interpolation of gaussian curve from limited points

    Hi, wonder if anyone can help me with something. I hope I can explain this... if I know a distribution is gaussian, can I determine the 'peak' from data either side of it? Obviously if I collected a lot of measurements and plotted them, I could see the trend of the curve, where the peak...
  20. M

    what is the PDF of magnitude and phase of this complex random number ?

    [/url][/IMG]i have a random variable as shown in the figure and i tried to find the PDF (probability density function )of the magnitude and phase of this random variable using central limit theory as i mentioned , i know that if we have complex random variable with both real and imaginary part...