mathematical expectation
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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
回答（2 个）
Walter Roberson
2012-1-6
0 个投票
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.
Gurudatha Pai
2012-1-6
0 个投票
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
2012-1-6
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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