c*********l 发帖数: 17 | 1 There's a set of terms {t1, t2, t3, ...}
probability for each is {P1, P2, P3, ...}
Now pick N terms from the set
What's the expectation (期望值)of number of unique terms?
请帮帮忙,多谢了 | X*****r 发帖数: 2521 | 2 没看懂啊
【在 c*********l 的大作中提到】![](/moin_static193/solenoid/img/up.png) : There's a set of terms {t1, t2, t3, ...} : probability for each is {P1, P2, P3, ...} : Now pick N terms from the set : What's the expectation (期望值)of number of unique terms? : 请帮帮忙,多谢了
| z*****n 发帖数: 7639 | 3 it should be something like if you pick a term N times,
what is the expected number of terms (amongst N terms) that
they are different to each other.
I think at least we need to know the size of the set...
【在 X*****r 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 没看懂啊
| c*********l 发帖数: 17 | 4 Yeah, we know the size of set, i.e. let's say M.
"pick N terms from the set": means just randomly pick N times from the set.
You may pick the same term multiply times.
【在 z*****n 的大作中提到】![](/moin_static193/solenoid/img/up.png) : it should be something like if you pick a term N times, : what is the expected number of terms (amongst N terms) that : they are different to each other. : I think at least we need to know the size of the set...
| y***u 发帖数: 101 | 5 Probability of t_i being picked uniquely = N P_i (1 - P_i)^(N-1)
Expected # unique terms = \sum_{i=1}^M N P_i (1 - P_i)^(N-1)
【在 c*********l 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Yeah, we know the size of set, i.e. let's say M. : "pick N terms from the set": means just randomly pick N times from the set. : You may pick the same term multiply times.
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