solve this problem im stuck in the question

QUESTION 3 (10 marks) Let (Xi)=1, n E N be independent identically distributed random variables, each following a density, parameterized by the parameter 0 E O = R given by f (2, 0) = 110,001 (20 ) e-(2-0) x ER, D E O = R. a) Consider a sample X = (Xi)?_, and calculate the the likelihood function L( (21 , . .., In), 0 ) = 112 1f(xi,0), 1, . . . , In ER. (2 marks) b) Which (if any) of the following statistics Ti : Rn -+ R, i = 1, 2,3 is sufficient? (3 marks) n Ti(21, . . ., n) = i= 1 n T2(21, . . ., n) = xi i=1 n T3(1, . . ., n) = (maxxi, -) In(lx:1)) i= 1 c) Determine a sufficient statistics with the lowest dimension