1.5 This exercise is a continuation of the example in Section 1.6.2 in which Y1,...,Yn are independent Poisson random variables with the parameter θ.

a. Show that E(Yi) = θ for i = 1,...,n.

b. Suppose θ = e

β

. Find the maximum likelihood estimator of β.

c. Minimize S = ∑

Yi −e

β

2 to obtain a least squares estimator of β.