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One obervation is taken from the probability model. f(x;θ)=((θ/2)^|x|)*((1-θ)^(1-|x|)) for x=-1,0,1 and θ ∈ [0,1]. We find...

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Statistics

One obervation is taken from the probability model.f(x;θ)=((θ/2)^|x|)*((1-θ)^(1-|x|)) for x=-1,0,1 and θ ∈ [0,1]. Wefind that the MLE of θ is |x|.

Now consider T(X) where T(X)=2 when x=1 and T(X)=0 otherwise.Show that the MLE of θ has a smaller variance than T(X).

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