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I have a poisson distribution with parameter lambda. X1,...,Xni.i.d. Poiss(), for some>0. And a estimator theta=ln(average(Yn)), where Yi=1 {Xi=0}, for i=1,...,n. How can i calculate

I have a poisson distribution with parameter lambda. X1,...,Xni.i.d. Poiss(), for some>0.

And a estimator theta=ln(average(Yn)), where Yi=1 {Xi=0}, for i=1,...,n.

How can i calculate the variance of the estimator theta?

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