3. LetX1,...,Xn iidN(,2). Let be the 95 percentile, i.e.P(X)=.95.

(a) Find the MLE of.

(b) obtain an exact(1 - a) CI for

(c)Suppose the data are

3.23 -2.50 1.88 -0.68 4.43 0.17

1.03 -0.07 -0.01 0.76 1.76 3.18

0.33 -0.31 0.30 -0.61 1.52 5.43

1.54 2.28 0.42 2.33 -1.03 4.00

0.39

Compute the MLE ^,compare standard error using the delta method, compute the standard error using the parametric bootstrap

In Exercise 3, assume X, 115i N(,u, 02). In Exercise 3(b), obtain an exact (1 oz) CI for T. Hint: E(S) 2 04(72):; for normal data, where 040;) = ,/%. In Exercise 3(0), modify the question as \"Compute the MLE 7?. Compute the standard error using the delta method. Compute the standard error using the parametric bootstrap.\