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May 24th, 2015, 07:18 AM  #1 
Newbie Joined: Nov 2013 Posts: 19 Thanks: 0  Seeking approximation method of a probability expression. Dear all, Given: $P^R_n(i) = \beta ^ \left( im \right) ( 1  \beta ) ^ \left( ni+m \right) \binom{nm}{im}$ and $\phi$ Want: $I^{min} _n = min \{ j: \sum_{i=j}^n P^R_n(i) < \phi \}$ I mean if there exists any simple ways of approximating or calculating the result of $\sum_{i=j}^n P^R_n(i)$. Or approximating $\sum_{i=j}^n P^R_n(i)$ withgut multiplying one after one of the multipliers of the factorial. 
May 24th, 2015, 04:13 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,685 Thanks: 661 
Your statement is somewhat confusing. What role does m have in $\displaystyle P_n^R(i)$?

May 24th, 2015, 08:06 PM  #3 
Newbie Joined: Nov 2013 Posts: 19 Thanks: 0 
$m$ is also a given number less than $n$.

May 24th, 2015, 08:31 PM  #4  
Newbie Joined: Nov 2013 Posts: 19 Thanks: 0  Quote:
I mean if there exists any simple ways of approximating or calculating the result of $\sum_{i=j}^n P^R_n(i)$. Or approximating $\binom{nm}{im}$ without multiplying one after one multipliers of the factorial.  
May 24th, 2015, 09:42 PM  #5 
Newbie Joined: Nov 2013 Posts: 19 Thanks: 0 
I think this website has been hacked, because I have found someone had modified my message!


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approximation, expression, method, probability, seeking 
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