Solution
= Solution
Part a applied to the deterministic kernel gives
$$
X_t\sim N\left(
xe^{-\lambda t},
\int_0^te^{-2\lambda(t-s)}ds\right)
=N\left(xe^{-\lambda t},
\frac{1-e^{-2\lambda t}}{2\lambda}\right).
$$
= Solution
Part a applied to the deterministic kernel gives
$$
X_t\sim N\left(
xe^{-\lambda t},
\int_0^te^{-2\lambda(t-s)}ds\right)
=N\left(xe^{-\lambda t},
\frac{1-e^{-2\lambda t}}{2\lambda}\right).
$$