意大利面条概率题

 

A plate of pasta contains 100 strands of spaghetti.

Tie two loose ends.

Keep doing this until there are no more loose ends.

What is the expected number of loops at the end?

 

 

 

所有跟帖： 

• IF E(1)=1, then E(n+1)=E(n)+1/(2n+1), So E(100)=1/199+1/197+1/19 -jinjing- ♀ (0 bytes) () 08/10/2012 postreply 13:51:59

• E(100)=1/199+1/197+1/197+.....+1/3+1=3.27869.... -jinjing- ♀ (0 bytes) () 08/10/2012 postreply 14:15:05

• 谢谢！忘了说请教啦！我再想想 E(n+1)=E(n)+1/(2n+1) -绿袖儿- ♀ (0 bytes) () 08/10/2012 postreply 15:32:18

• 谢题！We can get it when n=1,2,3 .if you are not mathematician. -jinjing- ♀ (0 bytes) () 08/10/2012 postreply 16:05:58

• E(1) = 1, E（n+1) = E(n) + 1. E(100) = 100. -wxcfan123- ♂ (449 bytes) () 08/11/2012 postreply 14:31:56

• 请注意,loops,100根有200个头,自成,loop概率1/199,所以E(100)=E(99)+1/199)*1 -jinjing- ♀ (40 bytes) () 08/11/2012 postreply 15:44:23

• 抱欠。将loops理解成程序中的多少次循环操作。职业性思维。 -wxcfan123- ♂ (0 bytes) () 08/11/2012 postreply 17:12:27

• 你是不是只考虑了一根的loops？但是几根也可以成loop -绿袖儿- ♀ (0 bytes) () 08/12/2012 postreply 18:48:26

• 细说一下递推公式，算是将功补过吧。 -wxcfan123- ♂ (264 bytes) () 08/12/2012 postreply 19:36:29

• 谢！我从来没有概率思维，搞不清各种情况。 -绿袖儿- ♀ (0 bytes) () 08/13/2012 postreply 07:26:16