A special case of a normal family is one in which the mean and the variance are
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(a) Find the LRT of H0: a = 1 versus H1: a =≠1 based on a sample X1,..., Xn from a n(θ, aθ) family, where θ is unknown.
(b) A similar question can be asked about a related family, the n(θ, aθ2) family. Thus, if X1,... ,Xn are iid n(θ,aθ2), where θ is unknown, find the LRT of H0 : a = 1 versus H1:α ≠ 1.
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