Timeline for A generalization of coupon collector problem - $\geq1$ pick per experiment
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 2, 2015 at 19:38 | history | edited | user76479 | CC BY-SA 3.0 |
added 121 characters in body
|
| Aug 22, 2015 at 0:50 | comment | added | user76479 | Instead of 1000 I took 499 or 498. I used mathematica. | |
| Aug 19, 2015 at 15:40 | comment | added | Max Alekseyev | @Arul: I do not understand what is 499 in here. Can you give numerical (integer) values of each of the parameters when the expression becomes negative? Just in case here is my PARI/GP code: { pr(T,S,N,k) = sum(i=0,T, (-1)^i * binomial(T,i) * binomial(T-i+S,N)^k ) / binomial(T+S,N)^k } | |
| Aug 19, 2015 at 2:26 | comment | added | user76479 | It is $>0$ at $499$, $<0$ at $498$. | |
| Aug 19, 2015 at 2:19 | comment | added | user76479 | I tried $k=Log2[1000]$, $T=N=(S+T)/k=1000/k$ in mathematica. Infact it goes to $<0$ if $10000$ replaces $1000$. | |
| Aug 19, 2015 at 2:06 | comment | added | Max Alekseyev | @Arul: What are your numerical values? The formula follows from the inclusion-exclusion principle. | |
| Aug 19, 2015 at 2:01 | history | edited | user76479 | CC BY-SA 3.0 |
added 92 characters in body
|
| Aug 19, 2015 at 1:55 | history | edited | user76479 | CC BY-SA 3.0 |
added 48 characters in body
|
| Aug 19, 2015 at 1:44 | comment | added | user76479 | @MaxAlekseyev I am not getting prob <1? Could you write your proof? | |
| Aug 19, 2015 at 1:32 | history | edited | user76479 | CC BY-SA 3.0 |
deleted 76 characters in body
|
| Aug 19, 2015 at 1:21 | comment | added | user76479 | @Henry Yes. $N=1$ is standard. What about $N>1$? | |
| Aug 18, 2015 at 20:16 | comment | added | Henry | If $N=1$ then the expectation is $(S+T)H_T$ | |
| Aug 18, 2015 at 18:42 | comment | added | Max Alekseyev | Not an asymptotic but exact answer for question 1: $$\binom{T+S}{N}^{-k} \sum_{i=0}^T (-1)^i \binom{T}{i} \binom{T-i+S}{N}^k.$$ | |
| Aug 18, 2015 at 15:28 | history | asked | user76479 | CC BY-SA 3.0 |