I need full answer instead of ChatGPT like response.\ \ Problem 2 (5 pts) Let

{x_(i):i=1,dots,n}

be a random sample from an exponential\ distribution with parameter

\\\\theta

, and probability density function\

f(x)=(1)/(\\\\theta )exp[-(1)/(\\\\theta )x]

\ where

\\\\theta in[0,\\\\infty ),xin[0,\\\\infty )

, and

E[x]=\\\\theta ,Var(x)=\\\\theta ^(2)

. The relevant loss function is\

L(p,d)=(n|\\\\theta -d|^(2))/(\\\\theta ^(2))

\ Consider exclusively unbiased rules, and assume that the smallest attainable risk among\ them is 1.\ Derive the ML estimator of

\\\\theta

; is it an optimal rule under these conditions? Is it\ minimax?

Problem 2 (5 pts) Let {Xi:i=1,,n} be a random sample from an exponential distribution with parameter , and probability density function f(x)=1exp[1x] where [0,),x[0,), and E[X]=,Var(X)=2. The relevant loss function is L(p,d)=2nd2. Consider exclusively unbiased rules, and assume that the smallest attainable risk among them is 1. Derive the ML estimator of ; is it an optimal rule under these conditions? Is it minimax