513设总体X~N(8,2),抽取样本X1,X2y…,X10,求下列概率: (1) PImax(X1,X2…,X10)>10l (2)Pmin(X1,X2y…,X10)<5 解:令X()=max(X1,X2x…X10),X()=min(X,X2”…X0) (1)P(X(m)>10)=1-P(X(m)10)=1-P(X1≤10) 810-8 =1-IP(X1≤10)=1-IIP(s )=1-①()=0.8224. 2 5-8 (2)P(X(0)<5)=1-1-()=0.4991. 2)( [min( ),...,, ]. )( [max( ),...,, ]; ,(~. ), ,,...,, 2 5 1 10 5.13 28 21 10 21 10 21 10 2 < > XXXP XXXP 设总体 NX 抽取样本 XXX 求下列概率： ([)()( )] .. ()( ([) )] .. ([)()()( )] max( ,...,, ), min( ,...,, ). )( )( )( )( )( 49910 2 85 2 115 8224011 2 810 2 8 1 110 1 110 110 10 10 1 10 10 1 10 1 10 1 21 10 1 21 10 = − −−=< =−= − ≤ − −=≤−= ≤−=≤−=> = = = = = Φ Π Π Φ XP X XP P XP XP XP X XXXX XXX i i i i i i n n n ∩ 解：令