概要信息：

‚‡ß¡ê K˜˜ ÷  Œ 	 Û ” m ; — — ĺ  
 kz˜ q 8 ˜  Ϙ 2   q 1 6 	1 . òåP (A) = 0.3, P (B |A)= 0.4, P (B |Ā ) = 0.5, P (B)= ____0 . 47______2 . òåÞí‹ ξ„Ʀýp: ϕ(x) =
{
k cosx, −
π
2
< x <
π
2
0, vƒ , k = _____ 12 ______3 . òå:ØÏξ„Œ¹î:Eξ =3, Dξ = 2, Eξ2 = _____1 1 ______4. 5P¡ÿ}ξá³sGÿ}: 1 000ö„p  ƒ„ÿ}Ž2000ö‚‡: _________1− e−2____________5 . Æc
„Ʀýp: ϕ0(x) = ___________ 1
2π
√ e
−
x2
2 _____________6 . òå ξŒ ηø’ìËξ∼N(1, 4), η∼N(2, 5)  ξ − 2η∼__N(−3, 24)___7 . ¾;S	 X 1 2 3
P θ2 2θ(1− θ) (1− θ)2  °½Ö¹Ï: 3„7,<(x1, x2,
x3): ( 1 , 2 , 1 ) , θ„'<60¡ θ̂: ______ 5
6
_______8 . Îc
;S N(µ, 4) -½Ö¹Ï: 9„7,< ( 1 , 6 , 1 0 , 3 , 5 , 2 , 8 , 9 , 1 ) . Ö α =
0.01 ùµ\:ô0¡—0ná:ô: ______( 3 . 283 , 6 . 7 1 7 ) ___________— ĺ Œ 
 U	˜ q 8 ˜  Ϙ 3   q 24 	1 . ùûU*,!7f  å Ah:Ö/'f  Bh:Ö/'Œf  ‹öAŒB/ ( B )( A) ùˋö ( B) ’¥‹ö( C) â/ùˋöÈ/’¥‹ö ( D) 
/ùˋö_
/’¥‹ö2 . кÏp ih  å
-Vçí-p  ô0-V:b åº;q-p!p ξ á³ ( C ) 1
( A) $¹ ( B) G ( C) àU ( D) c
3 . ¾:ØÏξŒ ηø’ìË  }˜
š˄/ ( D )( A) E(ξ + η)=Eξ +Eη ( B) E(ξη)=Eξ ·Eη( C) D(ξ − η)= Dξ +Dη ( D) D(ξη) =Dξ ·Dη4. 8Á_/́„Þí‹/ ( B )( A) p ( B) c
 ( C) G ( D) Γ5 . ôÕ
cn„/ ( B )( A) 'pš‹ô †'Ïø’ìË„:ØτG<„3š'( B) 'pš‹ô'Ïø’ìË„:ØτG<Ñ<Žc
( C) -ÁPšô †'Ïø’ìË„:ØτŒ„3š'( D) -ÁPšô'Ïø’ìË„:ØτŒÑ<Žc
6 . (pß¡-  ù;SXŒ7,(X1,
 , Xn)„ôÕê*/
cn„ ( D )( A) ;S/:ØÏ ( B) 7,/nC:ØÏ( C) X1,
 , Xnø’ìË ( D) X1 =X2 =
 =Xn7 . 7,sGpX̄*Å/;S<µ„ ( A )( A) '<60¡ ( B) 	H0¡ ( C) ô0¡ ( D) àO0¡8 . *åc
;S„µ ÀŒG¾H0: σ2 = σ0
2/&Ë  å	é„ß¡Ï/( C )( A) U =
X̄ − µ0
σ0/ n
√ ( B) T =
X̄ − µ0
S/ n
√ ( C) χ2 =
(n− 1)S2
σ0
2
( D) χ2 =
S2
(n− 1)σ0
2— ĺ 	 
 ¡—˜ q 4 ˜  Ϙ 1 0   q 40 	1 . ¾ŒC:ØÏ(ξ, η)„Th: ξ\η -1 0 10 0 1 /3 01 1 /3 0 1 /3 ( 1 ) BsŽ ξŒ η„¹ ( 2 ) $­ ξŒ η„ìË' ( 3 ) $­ ξŒ η„øs'  2
ã  ( 1 ) ¹: ξ 0 1
P 1 /3 2/3 , η -1 0 1
P 1 /3 1 /3 1 /3 . ------- 3( 2 ) 1 P (ξ =0, η =0) =
1
3
 1
9
=P (ξ =0)P (η = 0), å ξŒ η
ìË . ----- 6( 3 ) 1ThB— ξη„: ξη -1 0 1
P 1 /3 1 /3 1 /3 .àd	 cov(ξ, η) =E(ξη)−EξEη =0−
2
3
· 0 =0, àd ξŒ η
øs . --- 1 02 . ¾:ØÏξ∼N(1, 4) BP (−1< ξ < 5)ã  P (−1< ξ < 5) =Φ0
( 5− 1
2
)
−Φ0
( −1− 1
2
) ------------ 3
=Φ0(2)−Φ0(−1) ------------ 5
=Φ0(2) +Φ0(1)− 1 ------------ 8
=0.9773+ 0.8413− 1 = 0.8186 ----------- 1 03 . ¾ÏÑ®9}-Þ:„‚‡/0 . 2ø’ìË  °(Ñ1 00Ñ®9 ( 1 ) ("+
I0¡}-pî ξ(1 0Ñ0 3 0ÑKô„‚‡ ( 2 ) (-ÁPš0¡}-pî ξ(1 0Ñ0 3 0ÑKô„‚‡ ã  Eξ =np= 100 · 0.2= 20,Dξ = npq = 100 · 0.2 · 0.8= 16. ----- 2( 1 ) P (10< ξ < 30) =P (|ξ −Eξ |< 10)≥ 1−
Dξ
102
= 1−
16
100
= 0.84. -- 6( 2 ) P (10< ξ < 30)≈Φ0
(
30− 20
16
√
)
−Φ0
(
10− 20
16
√
)
=2Φ0(2.5)− 1= 2 · 0.9938− 1 = 0.9876 ------ 1 04. Îc
;SN(µ, σ2)-½ú7,¹Ï: 1 6„7,  ——vsGp: 3 1 60  Æî: 1 00  ÕÀŒG¾H0: µ= 3140/&Ë( α = 0.01 ) ã  ( 1 ) …ÀG¾ H0: µ= 3140. --------------------- 2( 2 ) 	Öß¡Ï T =
X̄ − µ
S/ n
√ ∼ t(n− 1). ------------- 4( 3 ) åh—0 tα = tα(n− 1)= t0.01(15)= 2.947. ----- 6( 4) ¡—ß¡< t =
x̄ − µ0
s/ n
√ =
3160−3140
100/4
= 0.8. -------- 8( 5 ) 1Ž |t|