MVUE for Exponential Family. Show that the family { p? } of (12.12) is a onedimensional exponential.

MVUE for Exponential Family. Show that the family { p_
} of (12.12) is a onedimensional exponential family, and derive the MVUE of
_ given n i.i.d. random variables drawn from P_ .

(a) Prove that T ( y) = max{y1,. . ., yn} is a sufficient
statistic for _.

(b) Prove that T ( y) is also complete. Note that you cannot
apply the Completeness Theorem for Exponential Families.

(c) Find an MVUE of _ based on y.