Variance of a vector product/sum combination

[nikozm]

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

 

[statdad]

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?

 

[nikozm]

Sorry for this typo. Let y be a 1 \times m vector instead.

Thanks

 

[statdad]

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?

 

[nikozm]

yes. and they are mutually independent random vectors. Do you have any clue ?