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Variance of a vector product/sum combination

  1. Dec 18, 2014 #1
    Hi,

    i am trying to find the variance of the following: y*(s+n), where y is a m \times 1 vector following a chi-squared distribution with 2k degrees of freedom, s is a m \times 1 vector following a Gaussian distribution with zero mean and unit-variance, and n is a m \times 1 vector following a Gaussian distribution with zero mean and variance z.

    Any help would be useful
     
  2. jcsd
  3. Dec 18, 2014 #2

    statdad

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    If y is [itex] m \times 1 [/itex] and both s, n are also [itex] m \times 1 [/itex], the product [itex] y \cdot (s + n) [/itex] is not defined: what are you trying to do?
     
  4. Dec 18, 2014 #3
    Sorry for this typo. Let y be a 1 \times m vector instead.

    Thanks
     
  5. Dec 18, 2014 #4

    statdad

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    Are they independent? and do you mean the variance/covariance matrix of [itex] s [/itex] is the identity matrix and that of [itex] n [/itex] is [itex] z [/itex] times the identity matrix?
     
  6. Dec 18, 2014 #5
    yes. and they are mutually independent random vectors. Do you have any clue ?
     
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