h******u
发帖数: 211 | 1 Here is the problem.
That is given N connected boxes (1-dimension), and M balls, suppose N>>M.
Randomly throw the N balls to the boxes and each ball has same probability
to be thrown to each of the box.
Each box can only hold one ball.
An isolated ball is defined as the ball with no other ball on its immediate
right or left.
Then the question is: What is the expected value of the number of the
isolated balls?
谢谢！ | w**********9
发帖数: 5 | 2 it is M when N>>M.
Sum[(i + 1)*Binomial[m - 1, i]*
Binomial[n - m - i + (i + 2) - 1, n - m - i], {i, 1, m - 1}]/
Binomial[n, m] | j******y
发帖数: 2578 | 3 any more detail about the derivation of the formula?
【在 w**********9 的大作中提到】
: it is M when N>>M.
: Sum[(i + 1)*Binomial[m - 1, i]*
: Binomial[n - m - i + (i + 2) - 1, n - m - i], {i, 1, m - 1}]/
: Binomial[n, m]
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