概率统计——习题十六解答 2.x=1x=996B2=1(x1-x)2=14259 ∑ B,=16296 3.(1)∵E(X)=E(X)=12,D(X)=4/5=0.8 12 √08N(01)2 PX-E()>l}=1-P(Xkl/√0.8} 1-[2Φ(1.118)-1=2[1-Φ(1.118)=0.2628 (2)P{min(X1…,X3)144=P{n>141032}=Pn>16}=0.10, (2)∵E(X-Y)=0,D(X-F)=0321032032 10156 (X-Y X N(O,1) 0.3/√6 P{x-Y|0.1}=1-P{(X-Y) 0.1 0.3/ 2-(6/3=21-d(08165)=0.4140 b 自由度为2 100
61 概率统计——习题十六解答 1．16。 2． = = = = = − = n i i n i i x x n x B n x 1 2 2 1 ( ) 1.4259, 1 99.96, 1 = = − − = − = n i i B n n x x n S 1 2 2 2 1.6296. 1 ( ) 1 1 3．(1) E(X) = E(X) = 12, D(X) = 4 / 5 = 0.8, ~ (0, 1), 0.8 * 12 N X X − = {| ( ) 1} 1 {| | 1/ 0.8} * P X − E X = − P X = 1 − [2(1.118) −1] = 2[1 − (1.118)] = 0.2628; (2) {min( , , ) 10} 1 {min( , ) 10} P X1 X5 = − P X1 X5 1 { 10, , 10} = − P X1 X )] 1 0.8413 0.5785. 2 10 12 1 { 10} 1 [1 ( 5 5 5 1 = − = − = − = − − i= P Xi 4．(1) = − = 10 1 2 2 ) ~ (10), 0.3 0 ( i Xi { 1.44} { 1.44 / 0.3 } { 16} 0.10; 2 1 0 1 2 = = = = P X P P i i (2) , 6 0.3 15 0.3 10 0.3 ( ) 0, ( ) 2 2 2 E X − Y = D X − Y = + = ~ (0, 1). 0.3/ 6 ( ) * N X Y X Y − − = } 0.3 / 6 0.1 {| | 0.1} 1 {| ( ) | * P X − Y = − P X − Y 1 {| ( ) | 6 / 3} * = − P X − Y = 2[1 − ( 6 / 3)] = 2[1 − ((0.8165)] = 0.4140. 5． , 2 100 1 , 20 1 a = b = 自由度为