$\alpha=P_2(X\ge1)=e^{-2}$ and $\beta=P_1(X<1)=1-e^{-1}$

Consider a single observation from $f(x;\theta)=\theta e^{-\theta x}$, $0<x<\infty$. Let $X\ge1$ be the critical region for testing $H_0:\theta=2$ against $H_1:\theta=1$. What are the values of type 1 and type 2 errors respectively?