What is second moment i-e $E[T^2]$ of random-variable: $T=\frac{1}{N}\sum\limits_{n=1}^N (X[n]+W[n])^2$,
Where $X[n]$ and $W[n]$ are both 'independent' of each other and 'stationary'. Moreover, $W[n]\sim \mathcal{N}(0,\sigma^2)$; however we only know the variance of $X[n]$ to be P (i-e $E[X^2]-E[X]^2=P$), and $E(X)=0$.
The first moment is $E[T]=P+\sigma^2$
But what would be second-moment $E[T^2]=??$
Need help ! Thanks.