We are given a random sample of size $n$ from an exponential distribution: $f(x;\theta)= \frac{1}{\theta} \exp{(-x/\theta)} I_{\{0,\infty\}}(x)$. Where $I_{\{0,\infty\}}(x)$ is the indicator function.
Then, my book says that it is "clear" that $I_{\{0,2\}}(x)$ is an unbiased estimator of $P(X\leq2)$.
How is it that this is so clear?
Thanks!