Recent content by trenekas

Oh my God. I made a mistake :) In the first line it should be ##r(0)*(r(0)−r(n−m))##

If I understand you I'll try to answer. ##r(n)## is covariance function of stationary process. ##r(n)## show the covariance between two random variables and ##n## is operator of distance. ##r(n)=EX_nX_0-EX_nEX_0## Because process X is stationary, then...

Hi all. My task is to prove the property of covariance function: ##(r(n)-r(m))^2≤2r(0)(r(0-r(n-m)))## My solution: ##1) (r(n)-r(m))^2=r(n)^2-2r(n)r(m)+r(m)^2## ##2) 2r(0)(r(0)-r(n-m)))=2r(0)^2-2r(0)r(n-m)## From covariance function properties I know that ##2r(0)^2≥r(n)^2+r(m)^2## So now I...

$$(I+\alpha uu^T)(I+xuu^T)=I$$ $$(I+I*xuu^T+I*\alpha uu^T+\alpha uu^T*xuu^T=I$$ So after that $$I*xuu^T+I*\alpha uu^T+\alpha uu^T*xuu^T=0$$ $$xuu^T+\alpha uu^T+\alpha uu^T*xuu^T=0$$ $$(x+\alpha) uu^T+\alpha*x (uu^T*uu^T)=0$$ $$(x+\alpha) uu^T=-\alpha*x (uu^T*uu^T)$$ And what's next...

ok i will try. thanks for help, Matterwawe!

I think here is need to use Woodbery formula, http://en.wikipedia.org/wiki/Woodbury_matrix_identity but i can't get the answer. :/

Hello. I need some help with one question about relationship of two matrices. The task: Suppose that I is identity matrix, u - is vector, u' is transposed vector, α - real number. It can be prove that inverse matrix of I+α*u*u' has similar form I+x*u*u'. The task is to find x. I tried to...

Hi there. I need some help to prove one equation. There is my solution but something is wrong i think. Any help would be appreciated :)

I found a solution :) Thank you.

Hi there. I would like to ask you one question about variance of estimator. Suppose that Y_i=βX_i+ε_i and β estimator is \bar{Y} / \bar{X}. I calculated mean of estimator. I am not sure if it's correct, but i got that its equal to n*β. But how about variance. Any help would be appreciated!

Hi all. I need to prove or disprove if process Y_n=1/2*X_n+1/4*X_{n-1}+1/8*X_{n-2} are stricly stationary. X_n,n\in R i.i.d. So almost i have the answer. But don't know if it is correct or not. I have a question of situation when \Gamma_Y(t,s) and |t-s|≤2 for example...

Hello, I have problem with one probability theory task. Hope that someone of you will be able to help me. So task is: Suppose that you are playing in lottery. The comptuer generates the lottery ticket which is made from 25 numbers. Total there are 75 numbers and 49 are extracted during the...

I want to ask, from where you get this: P(X>Y) = \int_{-\infty}^{\infty} G(y) f(y)\, dy, G(y) is cdf and f(y) density?

Also i have very similar question. Suppose that X,Y,Z are independent random variables and uniformly distributed in the interval [0;1]. What will be P(XY<Z^2) From that i know that density of all thre r.v. is 1 if xε[0,1] and 0 otherwise. So fx*fy=1 when x[0;1] and 0 otherwise. cdf of this...

So the answer is 1/2. hm :) ok