1 2 0.3 0.15 0.05 0.1 0 0.1 Çó(1) E(X).E(Y).D(X).D(Y). (2)cov(X,Y)¼°?XY.

½â ÈÝÒ×ÇóµÃXµÄ¸ÅÂÊ·Ö²¼ÎªP{X?0}?0.3,P{X?1}?0.45,P{X?2}?0.25; YµÄ¸ÅÂÊ·Ö²¼ÎªP{Y??1}?0.55,P{Y?0}?0.25,P{Y?2}?0.2, ÓÚÊÇÓÐ

(1)E(X)?0?0.3?1?0.45?2?0.25?0.95,

E(X2)?02?0.3?12?0.45?22?0.25?1.45

D(X)?E(X2)?[E(X)]2?1.45?0.95?0.5

(2)E(Y)?(?1)?0.55?0?0.25?2?0.2??0.15.

E(XY)?0?(?1)?0.1?0?0?0.2?0?2?0?1?(?1)?0.3?1?0?0.5?1?2?0.1

?2?(?1)?0.15?2?0?0?2?2?0.1

ÓÚÊÇ

14¡¢ÉèËæ»ú±äÁ¿XºÍYÏ໥¶ÀÁ¢, ÇÒX~N(1,2),Y~N(0,1),ÊÔÇó

?0.

cov(X,Y)?E(XY)?E(X)E(Y)?0.95?0.15?0.1425.

Z?2X?Y?3µÄ¸ÅÂÊÃܶÈ.

½â X~N(1,2),Y~N(0,1),ÇÒXÓëY¶ÀÁ¢, ¹ÊXºÍYµÄÁªºÏ·Ö²¼ÎªÕý̬·Ö²¼, XºÍ

YµÄÈÎÒâÏßÐÔ×éºÏÊÇÕý̬·Ö²¼, ¼´

Z~N(E(Z),D(Z)),

E(Z)?2E(X)?E(Y)?3?2?3?5, D(Z)?4D(X)?D(Y)?8?1?9, Z~N(5,32),

¼´ZµÄ¸ÅÂÊÃܶÈÊÇfZ(z)?132?e?(z?5)218,???z???.

15¡¢ÉèX1,?,X6ÊÇÀ´×Ô×ÜÌåN(0,1)µÄÑù±¾, ÓÖÉè

Y?(X1?X2?X3)2?(X4?X5?X6)2,

ÊÔÇó³£ÊýC, ʹCY·þ´Ó?2·Ö²¼.

½â ÒòΪX1?X2?X3~N(0,3)X4?X5?X6~N(0,3) X?X2?X3X?X5?X6ËùÒÔ 1~N(0,1),4~N(0,1), ÇÒÏ໥¶ÀÁ¢, ÓÚÊÇ

33 17

?X1?X2?X3??X4?X5?X6?2?????????~?(2),

33????2211¹ÊӦȡC?, ÔòÓÐY~?2(2).

3316¡¢Éè×ÜÌåX·þ´Ó±ê×¼Õý̬·Ö²¼, X1,X2,?,XnÊÇÀ´×Ô×ÜÌåXµÄÒ»¸ö¼òµ¥Ëæ»úÑù±¾, ÊÔÎÊͳ¼ÆÁ¿

?n?Y???1??5??i?15Xi2?Xi?6n2i,n?5

·þ´ÓºÎÖÖ·Ö²¼?

½â ÒòΪXi~N(0,1),

?i?15Xi2~?(5),

2?Xi?6n2i~?2(n?5),

ÇÒ

?Xi?152iÓë

?Xi?6n2i?XÏ໥¶ÀÁ¢, ËùÒÔ

i?152i5~F(5,n?5), ÔÙÓÉͳ¼ÆÁ¿YµÄ±í´ïʽ,

?Xi?6n2i(n?5)¼´µÃY~F(5,n?5).

17¡¢ÉèX~N(21,22),X1,X2,?,X25ΪXµÄÒ»¸öÑù±¾¡££¨??0.6??0.7257£©

Çó:(1) Ñù±¾¾ùÖµXµÄÊýѧÆÚÍûÓë·½²î; (2) P{|X?21|?0.24}. ½â (1) ÓÉÓÚX~N(21,22), Ñù±¾ÈÝÁ¿n?25, ?22?22??ËùÒÔX~N?21,?, ÓÚÊÇE(X)?21,D(X)??0.42.

25?25?(2) ÓÉX~N(21,0.42), µÃ

X?21~N(0,1), 0.4???X?21??0.6??2?(0.6)?1?0.4514. ¹Ê P{|X?21|?0.24}?P????0.4?18¡¢

ÔÚ×ÜÌåN(12,4)ÖÐËæ»ú³éÈ¡Ò»ÈÝÁ¿Îª5µÄÑù±¾X1,X2,X3,X4,X5.ÇóÑù±¾¾ùÖµÓë×ÜÌå¾ùÖµÖ®²îµÄ¾ø¶ÔÖµ´óÓÚ1µÄ¸ÅÂÊ.

½âÒòX122/5~N(0,1),¹ÊX122/552

P{|X12|1}1P{|X12|1}1P2[1(1.118)]2(10.8686)0.2628. 18