答案仅供参考
E(Y)??yipi?0.9
i∵甲机床生产的零件次品数多于乙机床生产的零件次品数，又∵两台机床的总的产量相同
∴乙机床生产的零件的质量较好。 4.2 解：X的所有可能取值为：3，4，5
P{X?3}?1CC35?0.1
P{X?4}?C3?0.3 35224P{X?5}?C3?0.6
C5E(X)??xipi?3?0.1?4?0.3?5?0.6?4.5
i4.3参见课本230页参考答案 4.4解：
P{X?n}?p(1?p)n?1,n?1,2,3......E(X)??xipi??np(1?p)n?1?in?1?p1?[1?(1?p)]2p
4.6参考课本230页参考答案
4.7解：设途中遇到红灯次数为X，则X~B(3,0.4)
E(X)?np?4?0.3?1.2
4.8解
答案仅供参考
??E(X)????f(x)xdx
1500 ?xdx??1(x?3000)xdx ??15001500300022015002 ?500+1000 ?1500
4.9参见课本后面230页参考答案 4.10参见课本后面231页参考答案 4.11 解:设均值为?,方差为
?2,则X~N(?,?2)根据题意有:
P(X?96)?1?P(X?96)
?1?P(X????96?72?)
?1??(t) ?2.3%
?(t)?0.997,解得t=2即?=12
所以成绩在60到84的概率为
P(60?X?84)?P(60-72X-?84-72??) 12?12)?(-1 ) ??(1-)1 ?2?(1--13 ?2?0.841 ?0.682 6
答案仅供参考
4.12E(X2)?0?0.4?12?0.3?22?0.2?32?0.1?2
E(5X2?4)?4?0.4?(5?12?4)?0.3?(5?22?4)?0.2?(5?32?4)?0.1?14
E(Y)?E(2X)??2xedx?2?xd(?e)?2[?xe00??x??x?x?04.13解：
|???0e?xdx]
?2(?e?x)|?20?2X?E(Y)?E(e)??e0??2x?xedx??e0??3x1?3x?1dx??e|?
0334?R34.14解：V?
3?1a?x?b?设球的直径为X,则：f(x)??b?a
其它??04?(E(V)?E(X3)2)?E(?X3)=b?x31dx???1?1x4b??(b?a)(b2?a2)?a6b?a6b?a4|a24364.15参看课本后面231页答案 4.16 解:
fx(x)??f(x,y)dy??12ydy?4x
3??0??x2fy(y)??f(x,y)dy??12ydx?12y?12y
??y????1223E(X)??E(Y)????ffx(x)?xdx??104xdx?344 54????y(x)?ydy??12y?12ydy?013 51xE(XY)?0?y?x?1??f(x,y)xydxdy?0?y?x?1??12xydxdy??300?12xydydx?31 2
答案仅供参考
E(X)??2????f(x)?xdx??22104xdx?452 35E(Y)??E(X 4.17解
22????f(y)?ydy??12y?12ydy?012 5?Y2)?E(X)?E(Y)?2216 15∵X与Y相互独立， ∴
1?21?E(XY)?E(X)E(Y)??x2xdx?ye5?ydy?(x3|)?yd(?e5?y)05305???222??(?ye5?y|??e5?ydy)??[5?(?e5?y)|]??(5?1)?4555 3334.18，4.19，4.20参看课本后面231，232页答案 4.21设X表示10颗骰子出现的点数之和，Xi(i?1,2,则X?10)表示第i颗骰子出现的点数，
?Xi?110i，且X1,X2,X10是
11?2??66121?66独立同分布的，又E(Xi)?1?1010?6?
所以E(X)?E(?Xi)??E(Xi)?10?i?1i?121?35 64.22参看课本后面232页答案
4.23E(X2)?0?0.4?12?0.3?22?0.2?32?0.1?2
D(X)?E(X2)?[E(X)]2?2?12?1
E(Y2)?0?0.3?12?0.5?22?0.2?32?0?1.3
答案仅供参考
D(Y)?E(Y2)?[E(Y)]2?1.3?0.92?0.49
4.24E(X2)??20x2424111111114xdx??x2(?x?1)dx?x4|?[?x4?x3]|?1??
224416016333D(X)?E(X2)?[E(X)]2?142?4? 33?1?x?1?1?11?xy?1?x?1dy??=?2 4.25fX(x)????14
其它??其它?0?0Var(X)?E(X2)?[E(X)]2??1111111??x3|??x2|? 23?122?131112xdx?[?xdx]2 ?12?121?1?y?1?1?11?xy?1?y?1dx??fY(y)????14=?2
其它??其它?0?0Var(Y)?E(Y2)?[E(Y)]2??113111211??y|??y|? 23?122?134.26因为X~N(0,4),Y~U(0,4)所以有Var(X)=4 Var(Y)=
1112ydy?[?ydy]2 ?12?1214 3故：Var(X+Y)=Var(X)+Var(Y)=4+
416= 33Var(2X-3Y)=4Var(X)+9Var(Y)= 4?4?9?4.27参看课本后面232页答案 4.28E(Z)?E(4?28 3X1?X2?n??Xn)?E(X1X)?E(2)?nn?E(Xn) n?11E(X1)?E(X2)?nn
11E(Xn)???n?? nn