X1, X2, .... ,Xn are independet exponential random variables with E(Xk)=k times lambda where k = 1,2,...,n. What is the sufficient statistics and maximum likelihood estimators of lambda??? and is it unbiased?

(a) sufficient statistics i got summation of Xk where k is from 1 to n

(b) MLE i got (1/n) times summation (Xk)/k where k is from 1 to n

(c) it is unbiased

Is my answers all correct??please reply me..thank you!!