北京工业大学2013-2014概率论与数理统计考题答案 - 百度文库 ر

ġ15֣Ϊ㷺һϣ֪ӪֵһֲҶҶᣬһάBвⶨҶҶẬķΪоص̲ҶẬǷ죬ѡ̲裬ÿص̲5Ʒ15ƷҶẬλmgԽ£

A ҶẬ A1 8.4 8.3 7.3 8.3 7.6

6.8 5.3 A2 5.4 7.4 7.1

9.8 8.4 A3 7.9 9.5 10.0

(1)ص̲ҶẬԲ죿ˮƽ??0.05 (2)ص̲ҶẬԲ죬ֵ?A1??A2ˮƽ

Ϊ95%䡣

: s=3,n1==n2=n3=5n=15

T?1??Xij?39.9, T?2??Xij?32 T?3??Xij?45.6

i?1i?1i?1n1n21n31T?????Xij=117.5 X?7.8333

j?1i?1snjsnjT?2ST???X??=947.31-920.4167=26.8933

nj?1i?12ijSA??j?1sT?2jT?2??=939.092-920.4167=18.6753 njnSE?ST?SA=8.218

з£ Դ ƽ A 18.6753 8.218 F0.05212=3.89 < F=13.6353, ܾH0

(2) X1?7.98X2?6.4

S??2?E?0.6848

n?st0.025(n?s)?t0.025(12)?2.1788

t0.025(16)SE(ɶ 2 12 9.3377 0.6848 Fֵ F=13.6356 112?)?2.17880.6848??1.1403 njnk5Ϊ

7.98-6.4?1.1403?1.58?1.1403?(0.4397,2.7203).

塢15֣˿Poisson̵ij̵꣬Ϊ??4/Сʱ̵֪900š

1930ʱһλ˿ͣ1130ʱܼѵ5λ˿͵ĸʡ 21000ʱλ˿͵£100ʱѵ10λ˿͵ĸʣ

3Poisson{N(t),t?0}ЭCN(s,t)дƵ̡

:tļʱλΪСʱ900Ϊʼʱ̡ (1)

15151P{N()?1,N()?5}?P{N()?1,N()?N()?4}222221?4?1 2e?4??4?24(4?2)1024?102}{e?{}?e?0.01551!4!3

(2)

P{N(4)?10,N(1)?2}P{N(1)?2}P{N(1)?2,N(4)?N(1)?8}P{N(1)?2}P{N(4)?N(1)?8}??P{N(1)?2}P{N(1)?2}P{N(4)?10|N(1)?2}?(4?3)8e?4?3??0.06658!

(3)CN(s,t)=?min{s,t},s,t>0,ԡ

15֣?Xn,n?0?Ϊʱ״̬ռI??0,1,2?һתƸʾΪ

?0.1?P=?0.9?0.1?0.20.10.80.7??0? 0.1??ʼֲPX0=0=0.3PX0=1=0.4PX0=2=0.3

(1)PX0=0,X1=1,X2=2 (2)PX0=1| X1=0, X2?2

(3)ж?Xn,n?0?ǷΪģ˵ɣDZģƽȷֲ ⣺

?0.26P2=??0.18??0.740.60.190.180.14?0.63?? 0.08??

1

P(X0?0,X1?1,X2?2)?P(X2?2|X1?1)P(X1?1|X0?0)P(X0?0)?0.63?0.6?0.3?0.1134

P(X0?1|X1?0,X2?2)?2

P(X0?1,X1?0,X2?2)P(X1?0,X2?2)P(X2?2|X1?0)P(X1?0|X0?1)P(X0?1)0.14?0.18?0.4???0.24P(X2?2|X1?0)P(X1?0)0.14?0.3

3P2 Ԫ ʱ

ƽȷֲΪ(?1,?2,?3)(?1,?2,?3)P=(?1,?2,?3)?1??2??3?1

817963,,) ƽȷֲΪ(223223223

ߡ15֣Z1Z2ǶֲͬP(Z1??1)?P(Z2?1)?12X(t)?Z1cos?t?Z2sin?tt?R֤X(t)ƽȹ̡

11⣺֪EZ1?EZ2??1??1??0

22E(X(t))?E(Z1cos?t?Z2sin?t)?cos?tEZ1?sin?tEZ2?0

112?(?1)2??12??1 ΪEZ12?EZ222Z1,Z2ĶԣEZ1Z2?EZ1EZ2?0 ʵã

RX(t,s)?E(Z1cos?t?Z2sin?t)(Z1cos?s?Z2sin?s)2?E(Z12cos?tcos?s?Z2sin?tsin?s?Z1Z2(cos?tsin?s?sin?tcos?s))

?cos(?(t?s))

ԣX(t)ƽȹ̡