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Topic: probability problem
Replies: 2   Last Post: May 4, 2013 11:34 AM

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Posts: 419
Registered: 10/7/06
Re: probability problem
Posted: May 4, 2013 11:34 AM
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On May 4, 1:43 pm, wrote:
> Hello,
> I am stuck with a probability problem. Here is the problem. Any help would be great.
> There are N samples each have probability of Pi (i=0......n-1)
> I want to find out probability of at least K of them occurs. Each is sampled only once. If probability of N events to be same it would have simpler. now since probability is different , not sure how to calculate this. Please also mention logic behind the calculations.

1. What's the result if K = 0? With that out of the way, assume K >=

2. Let q (i, j) be the probability that exactly j of the first i
samples occur, for 0 <= i <= n, 0 <= j < K. Let r (i) be the
probability that K or more of the first samples occur.

Given that K > 0, what is q (0, 0), what is q (0, j) for 1 <= j < K,
what is r (0)? Look at the definitions of q and r, and the result
should be obvious.

For 1 <= i <= n: Since you know q (i-1, j) for 0 <= j < K, r (i-1),
and p (i-1) which is the probability that the i-th sample occurs, how
do you calculate q (i, 0), q (i, j) for 1 <= j < K, and r (i) ?
There's a simple formula for each.

The desired result is r (n). Why?

3. For extra points: How do you reduce the number of calculations if K
>= n / 2?

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