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Material Type: Assignment; Class: Mathematical Statistics; Subject: Mathematics; University: Bucknell University; Term: Unknown 1989;
Typology: Assignments
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f (x; θ) = (1 − θ)xθ for x = 0, 1 ,... , 0 < θ < 1 (a) Show that Y = ∑ni=1 Xi is a sufficient statistic for θ. (b) Show that the sufficient statistic is a function of the MLE.
f (x; θ) = θ^2 xe−θx^0 < x < ∞, θ > 0. (a) Show that f is a regular case of the exponential family. (b) Find Y , a complete sufficient statistic for θ. (c) Compute E[1/Y ] and find a function of Y which is the unique MVUE of θ.