本题主要考查数列、概率、统计等基础知识,考查数据处理能力、运算求解能力,考查分类与整合思想、化归与转化思想
(Ⅰ)①ξ的可能取值为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912388226.gif)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912404217.gif)
,
P(ξ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912388226.gif)
)=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912435221.gif)
;
P(ξ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912404217.gif)
)=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912388226.gif)
;
P(ξ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912419222.gif)
)=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912435221.gif)
; -------------2分
ξ的分布列为
Eξ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912529763.gif)
------------
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/2014082314191288772.gif)
-----------------------5分
②设质点移到
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912903212.gif)
的概率为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912919220.gif)
,质点移到
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912903212.gif)
有两种可能:①质点先到
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912934226.gif)
,骰子掷出的点数为奇数,质点到达
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912903212.gif)
,其概率为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912981411.gif)
;②质点先到
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912997331.gif)
,骰子掷出的点数为偶数,其概率为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913012412.gif)
。
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913121618.gif)
(n≥4)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913137752.gif)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913153636.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912544687.gif)
--------------------------------------10分
法2:质点恰好到达
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912201208.gif)
有三种情形
①抛掷骰子四次,出现点数全为奇数,概率
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913277457.gif)
;
②抛掷骰子三次,出现点数二次为奇数,一次为偶数概率为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913293624.gif)
;
③抛掷骰子二次,出现点数全为偶数,概度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913309463.gif)
,故质点恰好到达
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912201208.gif)
的概
率
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141913371682.gif)
------------------------------------10分
(Ⅱ)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912279225.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823141912575233.gif)
……………………………………13分