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Thread: random vectors covariance

  1. #1
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    random vectors covariance




    If a random vector X = [x1,x2,...,xn]^T where T is the transpose has mean u and covariance R. Find the average and covariance of Y = b1x1+b2x2+...+bnxn where bi for i = 1 to n are scalar constants.

    E[Y] = u*sum of bi for i = 1 to n.
    cov(y) = E[YY']-E[Y]E[Y]' I am confused is E[YY'] = R ? but wouldnt YY' be scalar?

  2. #2
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    Re: random vectors covariance

    Please note that Y is a column vector.

    Therefore YY^T is an outer product which results in a matrix

    whereas Y^TY is an inner product which results in a scalar.

  3. #3
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    Re: random vectors covariance


    But isn't Y a scalar itself? or is each x1 a random vector too?

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