(Solved): Let (et) be a sequence of \( N(0,1) \) independent normal random variables. Let's examine \[ X_{t} ...

Let (et) be a sequence of \( N(0,1) \) independent normal random variables. Let's examine \[ X_{t}=e_{t}+\left(e^{2} t-1-1\right), \quad \mathrm{t}=1,2, \ldots \] a) Show that \( \mathrm{E}\left(X_{t}\right)=0 \); b) Show that \( \mathrm{E}\left(X_{t} X_{t+h}\right)=0 \) for \( \mathrm{h} \neq 0 \). Recall that \( E\left(e^{3}{ }_{t}\right)=0 \) because \( e_{t} \) is normal