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

1. \(E\left( {{Y}_{i}} \right)=\theta ,\,\,\,i=1,...,n\)
2. Suppose that \(\theta ={{e}^{\beta }}\). Find the maximum likelihood estimator of \(\beta \).
3. Minimize \(S=\sum{{{\left( {{Y}_{i}}-{{e}^{\beta }} \right)}^{2}}}\)

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