$$ E[X] = NQ $$
$$ X = \sum_{i=1}^N y_i^2$$
where $y_i$~$N(0,Q)$ and they are independent.
$$What \space is \space Var(X) ?$$
My understanding is:
$$ Var(X) = E[X^2]-E[X]^2 $$ But then what is $E[X^2]$ ?
I understand $X^2 = [ \space\sum_{i=1}^N y_i^2 \space ]^2$ But how do I compute $E[X^2] \space ?$
There appears to be a typo. Since $X=Q^2\chi^2$, the first line should read $$E[X]=NQ^2$$ by using the expectation of a $\chi^2$ distribution. To find the variance, use the variance of the $\chi^2$ distribution: $$V[X]=V[Q^2\chi^2]=Q^4V[\chi^2]=2NQ^4$$