# Variance of a vector product/sum combination

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?