Let X1, ...Xn be i.i.d. RV with density f(x)=

Problem 1. Let X1, ... Xn be i.i.d. random variables with density f (x) = (2 + 1)e-(+1)x if x 2 0 and f (x) = 0 otherwise. a. Find the MLE of 2. b. Find the asymptotic variance of the MLE of 2. c. Given that X1 = 1, X2 = 2, X3 = 3, X4 = 4, find an approximate 95% confidence interval for 2. Choose one of the following z-scores: z(0.025) = 1.96, z(0.05) = 1.64, z(0.1) = 1.28. d. Find the limiting distribution of 13, where 1 is the MLE from part a