Let (x_1, x_2, …x_n) be i.i.d. random variables that follow the Poisson distribution with parameter (lambda), i.e. (f(x;lambda)=dfrac{e^{-lambda}lambda^x}{x!}).
(10 points) Find the methods of moments estimator for (E[x_i]=lambda).
(10 points) Is this estimate unbiased? (show your work)
(10 points) Write an R function that would yield Methods of moments estimate for sample mean of a random sample of iid Poisson variables.
Argument: A vector of $X$ values
Output: MM estimate of $E[x_i]=lambda$
(5 points) Use your function and (x) defined below to calculate the MM estimate of (lambda).
set.seed(1)
x=rpois(100, 3.6)
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