Independence of two random variables having datasets

Question

Shankul Saini 2023-2-6

0
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https://ww2.mathworks.cn/matlabcentral/answers/1907145-independence-of-two-random-variables-having-datasets

评论： Shankul Saini 2023-2-9

Hi there, I hereby have two random varibles data sets names y1 and y2. I am stuck at the checking of their independence using matlab(or in any other ways), can someone help for the corresponding steps..

The correlation between these two random varibles is zero.

for ii=1:10^6
h=sqrt(0.5)*(randn(4,4)+1i*randn(4,4));
g=sqrt(0.5)*(randn(4,4)+1i*randn(4,4));
y=g*h;
y1(ii)=y(1,1);
y2(ii)=y(1,2);
end

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Answer 1

Dongyue 2023-2-8

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https://ww2.mathworks.cn/matlabcentral/answers/1907145-independence-of-two-random-variables-having-datasets#answer_1166805

在 MATLAB Online 中打开

If two vactor x and y are linearly dependent, there should exist ax + by = 0, so you only have to check:

clear; clc;
result = true;
for ii=1:10
    h=sqrt(0.5)*(randn(4,4)+1i*randn(4,4));
    g=sqrt(0.5)*(randn(4,4)+1i*randn(4,4));
    y=g*h;
    %check whether xi1/xi2==yi1/yi2     
    if real(y(1,1))/imag(y(1,1)) ~= real(y(1,2))/imag(y(1,2))
        result = false;
        break
    end
end
result
result = logical
   0