Let yi n i=1 be independently-observed non-negative integers drawn from a poisson distribution. It has the following probability mass function:
f(yi |θ) = θ yie −θ/yi!
where yi! = yi × (yi − 1). . . × 3 × 2 × 1 is the factorial.
The Poisson distribution has the properties E(yi) = 0 and E(y²i) = 0² +0. 1.
Find the method of moment (MM) estimator of using only the first moment condition E(yi) = 0.