Pstat 127 HW4 Q2 sol.pdf - W18 Homework 4 solution Q2 2 Suppose Yi has density in the exponential family form used in class for i cfw_1 n Assume the

# Pstat 127 HW4 Q2 sol.pdf - W18 Homework 4 solution Q2 2...

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2. SupposeYihas density in the exponential family form used in class, fori∈ {1, . . . , n}. Assume the formulae I wrote on the board inlecture forE(Yi)andV ar(Yi)for a random variable following such an exponential family distribution, namely thatE(Yi) =b0(θi) =∂ b(θi)∂θiandV ar(Yi)=ai(φ)b00(θi) =ai(φ)2b(θi)∂θ2i.For each of the following 3 distributions (each of which we wrote in this exponential family form during lectures), first review all thesteps that we used in writing these in exponential family form, and then show that these mean and variance formulae provide the samemean and variance that you know from previous courses in each case.(a) IfYiN(μi, σ2), show that these formulae provide the same mean and variance that you know from previous courses.