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】
: 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】
: 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】
: 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】
: 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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