Problem 3 (10 points ). Let X Xz, .... Xn ild N (100, 102), 1=10, 0=10,5210. ( a) Find P(X, >120 ), note XI~N( 100, 10-), X, is not an order statistic (b). Consider n = 30, X130) = max ? X Xz, 2 Xsoy. Find P( X( 30) >120) ( c). Using simulation method to approximate above probability P(X(30)>/ 20). In specific; simulate K= 10,000's X(so ) using "for" loop in R, calculate the proportion of X130 ) which is greater than 120 among above 10,000's X30 ) . Compare your result from your simulation study with your theoretical value of P(X (30) 2120 ) in part (b). ( d ) Repeat parts ( 6) and ( c) with n-100, ie. find P(X(109)>120) using both andytical and simulation methods. Comment your results