Question: 5. Assume that \({{Y}_{1}},...,{{Y}_{n}}\) are independent Poisson variables with parameter \(\theta \)

(a) \(E\left( {{Y}_{i}} \right)=\theta ,\,\,\,i=1,...,n\)

(b) Suppose that \(\theta ={{e}^{\beta }}\). Find the maximum likelihood estimator of \(\beta \).

(c) Minimize \(S=\sum{{{\left( {{Y}_{i}}-{{e}^{\beta }} \right)}^{2}}}\)