Variance of a vector product/sum combination

  • Thread starter nikozm
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  • #1
nikozm
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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
 

Answers and Replies

  • #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?
 
  • #3
nikozm
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Sorry for this typo. Let y be a 1 \times m vector instead.

Thanks
 
  • #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?
 
  • #5
nikozm
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yes. and they are mutually independent random vectors. Do you have any clue ?
 

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