mathematical expectation

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PChoppala
PChoppala 2012-1-6
评论： Ibrahim ATA 2021-11-6
Hi
Suppose we have a vector X=[1 2 -1 5 2], I want the mathematical expectation E{x*x'}, can you please help me with that statements?
I presume the result will be a 5X5 matrix! This matrix is also called as the correlation matrix(as defined by the author of the paper I am doing).
Cheers
P

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回答（2 个）

Walter Roberson
Walter Roberson 2012-1-6
With your given X, X*X' would be a 1 x 1 matrix.
If your X was instead [1 2 -1 5 2].' then X*X' would be a 5 x 5 matrix. To phrase this another way, use a column vector instead of a row vector.
  2 个评论
PChoppala
PChoppala 2012-1-6
Brings me closer, but the authors call it mathematical expectation.
X=[1 2 -1 5 2]', and
I use x*x', so I get a 5X5 matrix.
But what is a mathematical expectation here? and still the result should be a 5X5 matrix!
I assume 'mean(x*x')' is not right!
Or E{x*x'}=x*x'? In my example, x is a vector having complex exponential.
Please advice
Ibrahim ATA
Ibrahim ATA 2021-11-6
So how to apply expectation operator ?

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Gurudatha Pai
Gurudatha Pai 2012-1-6
As you have given it, you are only calculating the outer-product and not the covariance. To calculate the covariance you need more information than one data point. The best information you could have is the probability density function of the random vector X. At the least you need to have many samples of the random vector to calculate the sample statistics and if you have enough number of samples, you may hope to (because there are other conditions) reach the true co-variance.
  2 个评论
PChoppala
PChoppala 2012-1-6
Yep, I have many samples for the vector(signal) x. Say x is a column vector of 100 or 1000 elements.
Then how?
Walter Roberson
Walter Roberson 2012-1-6
See http://www.mathworks.com/help/toolbox/stats/corr.html
but note that what you need on input is (something) by 5 in order to get out a 5 x 5 result. If you are starting from a vector, you cannot get a 5 x 5 correlation matrix: your input needs to be the list of samples, one sample per row, one column per parameter.

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