4. A random sample $X_1, X_2, \ldots, X_n$ of size n is taken from a Poisson distribution with a mean of $\lambda, 0 < \lambda < \infty$. Show that $\bar{X}$ is the minimum-variance unbiased estimator for $\lambda$. (15%)

4. A random sample X_1, X_2, , X_n of size n is taken from a Poisson distribution with a mean of λ, 0 < λ &

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4. A random sample X_1, X_2, , X_n of size n is taken from a Poisson distribution with a mean of λ, 0 < λ < ∞. Show that X is the minimum-variance unbiased estimator for λ. (15%)

4. A random sample $X_1, X_2, \ldots, X_n$ of size n is taken from a Poisson distribution with a mean of $\lambda, 0 < \lambda < \infty$. Show that $\bar{X}$ is the minimum-variance unbiased estimator for $\lambda$. (15%)

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