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...
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 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...
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...