program编程语言代做、Python，Java，c/c++程序设计代写

日期：2020-11-05 11:31

Assignment 2. Due: Nov 10, 2020, 11:30pm

1. Let X1, . . . , Xn be a random sample from a geometric distribution that has pmf f(x|θ) =

(1?θ)

x

θ, x = 0, 1, 2 . . ., 0 < θ < 1, zero elsewhere. Show that Pn

i=1 Xi

is a sufficient statistic

for θ.

2. Let X1, . . . , Xn be a random sample from a Beta(θ, 5). Show that the product X1×· · ·×Xn

is a sufficient statistic for θ.

3. Write the pdf, 0 < x < ∞, 0 < θ < ∞,

zero elsewhere, in the exponential form. If X1, X2, ..., Xn is a random sample from this

distribution, find a complete sufficient statistic Y1 for θ and the unique function φ(Y1) of this

statistic that is the MVUE of θ. Is φ(Y1) itself a complete sufficient statistic?

5. Let X1, . . . , Xn be a random sample from a uniform distribution [0, θ], for some unknown

parameter θ > 0. Is X(n)

, the largest order statistic among all samples, a sufficient statistic

for θ?

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