mathematical expectation

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PChoppala on 6 Jan 2012
Commented: Ibrahim ATA on 6 Nov 2021
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).

Answers (2)

Walter Roberson
Walter Roberson on 6 Jan 2012
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.
Ibrahim ATA
Ibrahim ATA on 6 Nov 2021
So how to apply expectation operator ?

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Gurudatha Pai
Gurudatha Pai on 6 Jan 2012
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.
Walter Roberson
Walter Roberson on 6 Jan 2012
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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