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## Homework Statement

For a random sample [tex]X_{1}, ..., X_{n}[/tex] from the Poisson distribution, find an unbiased estimator of [tex]\kappa\left(\theta\right) = \left(1 + \theta) e^{-\theta}[/tex].

## The Attempt at a Solution

I know that the pmf of Poisson distribution is [tex]f\left(x; \theta\right) = \frac{e^{-\theta}\theta^{x}}{x!} I_{(o, 1, ...)}\left(x\right)[/tex]

The parameter is [tex]\theta[/tex], but I do not know how to find the unbiased estimate of this problem.