Let x₁,...,xn € Rd. Let y₁,..., yn be independent Poisson random variables satisfying E[yi] = e(xi,w), for some unknown w E Rd. Consider the problem of estimating w given x₁,..., xn and y₁,..., yn. 1. Show that the maximum-likelihood estimator ŵn for w is given by 1 n Σ-Yi (xi, w) + e(x₁,w). i=1 Vl≤i≤n, ŵn E argmin fn(w), fn(w):= === WERD n

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