c*******r
发帖数: 1 | 1 I have an easier solution as follows:
Let T be the survival dates and X(i)=Indicator(was hurt on the ith day),
i=1,2,...
Let E[*] denote the expectation.
Observe that
E[T|X(1)=0]=1+E[T]: if the first day was not hurt, the expectation should be 1
day more.
E[T|X(i)=0, i=1,2]=2+E[T]. and so on.
By conditional expectation:
E[T]=E[T|X(1)=0]*1/2+E[T|X(1)=1,X(2)=0]*1/2^2+E[T|X(1)=1,X(2)=1,X(3)=0]*1/2^3+
...+E[T|X(i)=1,i=1:20]*1/2^20.
So x=(1+x)/2+(2+x)/2^2+(3+x)/2^3+...+ (20+x)/2^20 +20*1/2^20.
x=E[T] |
|
