Re: [CFRG] Combinitorics probabilities

[Robert Moskowitz <[e-mail]>]

On 8/8/22 17:16, Robert Moskowitz wrote:
>
>
> On 8/8/22 17:07, Dan Brown wrote:
>> I think you want:
>> https://en.wikipedia.org/wiki/Binomial_distribution#Tail_bounds
>
> Pretty heavy lifting and it does not read like my problem.  Then I 
> read the intro:
>
> The binomial distribution is frequently used to model the number of 
> successes in a sample of size n drawn with replacement from a 
> population of size N. If the sampling is carried out without 
> replacement, the draws are not independent and so the resulting 
> distribution is a hypergeometric distribution, not a binomial one. 
> However, for N much larger than n, the binomial distribution remains a 
> good approximation, and is widely used.
>
>
> I believe this is "without replacement" and N is close to n.
>
> e.g.: 5 messages are sent.  You want to receive at least 3 of them; 
> any 3 and more is ok.  The probablity of receiving any one message is 
> p...
>
> So off to look at hypergeometric distribution?

No not hypergeometric.  Back to binomial.

Fun!  This is stuff I learned back around '69 or '70!  Where are those 
brain cells hiding?

I had enough stat then that I could have degreed in it, but I did not 
consider it fun...

Maybe I burned those cells after getting my comp sci degree?

:)

>
>
>> Best regards,
>> Dan
>>
>>> -----Original Message-----
>>> From: CFRG <[e-mail]> On Behalf Of Robert Moskowitz
>>> Sent: Monday, August 8, 2022 4:59 PM
>>> To: [e-mail]
>>> Subject: [CFRG] Combinitorics probabilities
>>>
>>>   CAUTION - This email is from an external source. Please be 
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>>> links
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>>>
>>> Well I spent the afternoon googling, but my search foo is weak.
>>>
>>> I want the formula for the probablity of receiving at least m out of n
>>> messages
>>> given the probablity of receiving any message is p.
>>>
>>> I did find:
>>>
>>> https://urldefense.com/v3/__https://www.statology.org/probability-of-at- 
>>>
>>> least-
>>> two/*:*:text=P(X**B2)*20*3D,(X**B2)*20*3D*200.3673__;I37iiaUlJeKJpSUlJQ
>>> !!JoeW-IhCUkS0Jg!cUlR8MdsZ0VvH1GymBznGvOigS-
>>> vQjTeU2LxJmllO1oVh8_GNKrvuam52NbSOIT2KzNggbgkbpzkfqyWTupj$
>>>
>>> But this is a series to find the final answer, not the 'final' formula.
>>>
>>> So for example to receive at least 2 out of 3 messages where the 
>>> probablity
>>> of
>>> any message at 95% comes out to 97.2%
>>>
>>> But what about 3 out of 5?  etc.
>>>
>>> Pointer is greatly appreciated.
>>>
>>> I took stat just too many decades ago, and I have not kept that 
>>> knife sharp.
>>>
>>> thanks
>>>
>>>
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