Variance of a vector product/sum combination

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
 
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If y is m \times 1 and both s, n are also m \times 1, the product y \cdot (s + n) is not defined: what are you trying to do?
 
Sorry for this typo. Let y be a 1 \times m vector instead.

Thanks
 
Are they independent? and do you mean the variance/covariance matrix of s is the identity matrix and that of n is z times the identity matrix?
 
yes. and they are mutually independent random vectors. Do you have any clue ?
 

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