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(Solved): Let X1,...,Xn Be A Sample Of Iid Exp(𝜃1,𝜃2) Random Variables With Common Pdf For And . A) Show...

Let X1,...,Xn be a sample of iid Exp(𝜃1,𝜃2) random variables with common pdf f(x; 61, 62) = = 1 for I > 0 and =RXR+ .

a) Show that 7*(1)x)=s is jointly sufficient for (𝜃1,𝜃2).

b) Determine the pdf of X_{(1)} .

c) Determine EX(1)

d) Determine E[X]

e) Determine Var X (1)

f) Is X_{(1)} an MSE-consistent estimator of 𝜃2?

g) Given 7*(1)x)=s is a complete sufficient statistic for (𝜃1 , 𝜃2 ), determine the UMVUEs of 𝜃1 and 𝜃2.

f(x; 61, 62) = = 1 I > 0 =RXR+ 7*(1)x)=s EX(1) E[X] Var X (1)

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