Show, by direct computation or using the moment generating function (20.10), that the variance of the compound Poisson process \(Y_{t}\) with intensity \(\lambda>0\) satisfies

\[\operatorname{Var}\left[Y_{t}\right]=\lambda t \mathbb{E}\left[|Z|^{2}\right]=\lambda t \int_{-\infty}^{\infty} x^{2} u(d x)\]