Problem 1I* (MLE for the Poisson distribution). Consider n i.i.d. random variables, each of them Poisson(1), with unknown parameter A. Suppose that we measure the values X1 = x1, X2 = 22, ..., Xn = Xn. The likelihood function is e(1) = f(kil)).. . .. f(kn|)), where f(k )) = e-1Ak k! , with k = 0, 1, 2, 3, .... Find the value of A that maximizes the probability of the data, i.e. the maximum likelihood estimate AML. This is done by first computing the log-likelihood L(A) = log ((1), by setting L'(A) = 0 and solving for 1. Why is the result not that surprising? (Remember that if Xi ~ Poisson()), then E(Xi) = 1.)