习题
8.解:令X 表示命中敌机的子弹数,则:
()500*0.015X
P λ==
()55
55!50.1755e P X -===
9.解:令X 表示断纱次数,则
()1000*0.0044X
P λ==
()410
4!0
100.9972i
e i i P X -=≤==∑
10.解: (1)()4848!
80.0298e P X -==
=
(2)()()410
4!
1011010.0028i e i i P X P X -=>=-≤=-
=∑
$
习题
3.解: (1)由()2
2
1cos 2x dx A xdx A π
π?∞
-∞
-=
==?
?得,A=1/2
(2){
}4
142
0cos 0.3536P x xdx π
π
<<
==
≈?
5.解:令Y 表示损坏的真空管数,则
()()()()()
2
1001503
08233272121
4333
9
1502/3
01x
P X dx P Y C P Y C +∞
>=====
===
?
6.解: (1)
()1000
110001000
10001/0.368x P X e
dx e +∞
->==≈?
(2)令Y 表示损坏的电子管数,则所求概率为: -
()()5
01/0.0067489P Y e ==≈
7.解:要使方程有实根则:
()()()2
2444216216(2)(1)0K K K K K K ?=-??+=--=-+≥,
即2,1K K ≥≤-
由题意知:
()()523
55
21P K P K -≥+≤-== 即方程有实根的概率为3/5.
8.解:
()15215
1010x P X e
dx e ∞
-->==?
则
\
()
()()()
2
2
2
15115
5,1,0,1,2,...,5
e i
i
i e e Y
P P Y i C
i -==-=
()()(
)
2
5
1110110.5167e P Y P Y ≥=-==--
=
习题
4.解:
(1)由:()()()()22=1 1=0 2F A B F A B ππ
+∞=+??
??-∞=-???
解得:A=1/2,B=1/π (2){}()()11111/2P X F F -<<=--= 5.
{}()()()()()()5323
222510.5110.50.5328
P X --<≤=Φ-Φ=Φ-Φ-=Φ-+Φ={}()()()()()1034322410 3.5 3.52* 3.510.9996P X ----<≤=Φ-Φ=Φ-Φ-=Φ-=
{}{}{}{}{}()()
()()2323222221221 =1-1+0.51 2.50.697
P X P X P X P X P X --->=>+<-=-≤+<-=-Φ+ΦΦ+-Φ={}{}3130.5P X P X >=-≤=
(2)
{}{}()()()(){}
2343
22212110.50.54P X P X P X -->=-≤=-Φ=-Φ-=Φ=Φ=≤ '
6.解:所求概率为:
{}()()()()()()10.050.1210.0610.050.1210.06
0.060.06
110.050.1210.050.121 1222120.0456
P P X +---=--≤≤+=-Φ+Φ=-Φ+Φ-=-Φ=
习题
由1y =()()3
1x y
h y =-=,其导数为:
()()2
'31h y y =--
故,Y 的概率密度为:
()()
()
(
)
6
2
1
1131y y y π?+-=-
6.解:由24
y x π=
得:()x h y ==
()'
h y =
()()2549y Y ?ππ=
≤≤
&
总习题二
4.解:
(1){}21200
200
1
1000
110.005x x
P x e dx e --<=
=-=? (2){}252*52
200
200
10052
520x x P x e dx e
--∞
>=
=≈?
5.解:(1){}()2
2
75
1
499
2727
114P x x dx >=
-=
-=
?
(2)()()
()
10522
102727i
i
i
P Y i C -==,i=0,1,2,…,10
6.解:
(){}{}{}{}()()()()2
2
2
2arcsin arcsin 'sin arcsin arcsin =
1(10)
y y Y F y P Y y P X y P X y P X y y y F y ππππ?-=≤=≤=≤+≥-+-
≥≥==
%