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Suppose that the number of accidents occurring daily in a certain plant has a Poisson distribution with an unknown mean $\lambda$. Based on previous experience in similar industrial plants, suppose that a statistician's initial feeling about the that possible value of $\lambda$ can be expressed by an exponential distribution with parameter 2. What are the two Bayes estimates of $\lambda$?

I tried to find the posterior density, but I got stuck at: $$f(\theta|X_1,...,X_n) = \frac{k}{\int_0^\infty k d\theta}$$ where $k = e^{-(n+2)\theta}\theta^{X_1+...+X_n}$. I'm not sure if I did this right and if I did, I don't know how to integrate the denominator of that fraction.

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