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(Solved): Let X1,...,Xn Be A Sample Of Iid Exp(ðœƒ1,ðœƒ2) Random Variables With Common Pdf For And . A) Show...

Let X1,...,Xn be a sample of iid Exp(ðœƒ1,ðœƒ2) 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 (ðœƒ1,ðœƒ2).

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 ðœƒ2?

g) Given 7*(1)x)=s is a complete sufficient statistic for (ðœƒ1 , ðœƒ2 ), determine the UMVUEs of ðœƒ1 and ðœƒ2.

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

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(Solved): Let X1,...,Xn Be A Sample Of Iid Exp(ðœƒ1,ðœƒ2) Random Variables With Common Pdf For And . A) Show...