(a) Write the log-likelihood function for the Poisson distribution, given data \(x_{1}, \ldots, x_{n}\), corresponding to the likelihood function in equation (4.26).

\(L\left(\lambda ; x_1, \ldots, x_n\right)=\lambda^{\sum_{i=1}^n x_i} \mathrm{e}^{-n \lambda} \prod_{i=1}^n \frac{1}{x_{i}!} \tag{4.26}\)

(b) Determine the MLE of \(\lambda\).