題組內容

3. (20%) A random sample \( X_{1}, X_{2}, \ldots, X_{n} \) of size \( n \) is taken from a Poisson distribution with a mean of \( \lambda \), \( 0 < \lambda < \infty \).

(a) \( (15\%) \) Find the maximum likelihood estimator for \( \lambda \), and prove it.