SOlve the following question manually

(6 points) (Please give your answer to four (4) decimal places where needed.) Let X1, ,Xn be a random sample from a continuous distribution with pdf 29xex (0x2), 0 S x 0, and E(X) =1 (419 Var(X) = 4;; . From an observed sample of size n = 5, we calculate 2L1 xi = 14 and 2;] x? = 52. (a) (1 MARK) (True or False): fx(x|6) is an exponential family of distributions. A. True 0 B. False (b) (1 MARK) (True or False): 2;] X; is a complete sufficient statistic for 9. O A. True 0 B. False (c) (1 MARK) Based on the observed sample, calculate the Method of Moments estimate of 19: (d) (2 MARKS) Based on the observed sample, calculate the Maximum Likelihood Estimate (MLE) of 6: (e) (1 MARK) Based on the observed sample, calculate the Maximum Likelihood Estimate (MLE) of Var(X)