3. LetX1,...,Xn iidN(,2). Let be the 95 percentile, i.e.P(X )= 0.95.

(a) Find the MLE of .

(b) obtain an exact( 1 - a) CI for .(Hint for the picture)

(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.....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.\