Unbaised estimator of $\ e^{- 2 \lambda } $ is t(x) = $ \ (-1)^x $ Prove that
Unbaised estimator of $\ e^{- 2 \lambda  } $ is t(x) =  $ \ (-1)^x $  ,
when x follows poisson distribution with parameter $\lambda $
Sorry to ask the direct question but I need a starting hint to solve the question , actually last time I studied statistical inference was 1 year back , I would be great if anyone could just give some starting steps .

E $\ (-1)^{x} $ = $ \frac {\sum_{x=0}^{ \infty} (-1)^{x} \ e^{- \lambda } \lambda^{x} }{\ x! } $
= $ e^{- \lambda } $ $ \frac {\sum_{x=0}^{ \infty } (- \lambda )^{x}}{ x !} $
{ this is the property of exponential function }
= $ e^{- \lambda } $ $ e^{- \lambda } $
= $ e^{- 2\lambda } $
