Stanton D. answered • 05/31/20
Tutor to Pique Your Sciences Interest
Hi Weyland R.,
I can't get you all the way through, but the start of this problem is perhaps recognition that the initial setup condition is a Poisson distribution on 330,000,000 events, and that all of them (that's the start time events) must have occurred. Then, the integration proceeds to recognize that none of the end time events have occurred for (all but one of) these 330,000,000 event sets. I'd assume that's another Poisson distribution integration, though I don't know how to set it up. This combined probability relationship is integrated over the entire interval. My guess would be, don't count on it happening within the age of the universe, etc.
-- Cheers, -- Mr. d.
Stanton D.
You can model the data, with not much difficulty. I used LibreOffice. Run two columns as RND(), then 2 more columns to sort into MIN and MAX respectively (start and stop times for the call attendance, on the (0,1) interval). Then, roughly bunch the range, such as into 0.1 steps, and set up logical Boolean test: (end>range_beginning&start_range_end)[note: this seems contraintuitive, but it's easiest!)->numeric (0 or 1) output (in LibreCalc, that's the "NUM" conversion function) across the steps x range output area. The pattern of 1's shows if the rnd "call" is on anywhere in that step time. You may then either 1) sum the column values (shows the bulk attendance at that time interval). The bulk_on distribution is gently domed, with P~0.2 at the ends (but, that's with 0.1 step size; actually it must ->0 at the ends as a continuous function) and a max ~ 0.75 around t=0.5. or 2) product the column data (LibreOffice requires typing all cells for that, so you won't want to do it much!). Tests with just the first 4 callers showed a "hit" about 1/2 the trials, but with the first 10 callers, NO HITS in 11 trials. So I think that scales as the exponent(in #people) of P(bulk _not_on_the_call), which is astronomically small in your problem -- at best, ~0.75^330,000,000 or whatever. Do it by logs! And 2 people, would be the same, because the problem did specify that everyone else was on the call!! --Cheers, this was a fun problem to work on, --Mr. d.02/09/22
Stanton D.
By the way, sorry about Wyzant text modifications above. If you dont already know, it transforms most non-letter symbols into ampersand plus codes. Think you can decipher, except possibly where there is a Boolean-logical-and in the original text. I cant figure out what it did there.02/09/22
Stanton D.
You can model the data, with not much difficulty. I used LibreOffice. Run two columns as RND(), then 2 more columns to sort into MIN and MAX respectively (start and stop times for the call attendance, on the (0,1) interval). Then, roughly bunch the range, such as into 0.1 steps, and set up logical Boolean test: (end>range_beginning&start_range_end)[note: this seems contraintuitive, but it's easiest!)->numeric (0 or 1) output (in LibreCalc, that's the "NUM" conversion function) across the steps x range output area. The pattern of 1's shows if the rnd "call" is on anywhere in that step time. You may then either 1) sum the column values (shows the bulk attendance at that time interval). The bulk_on distribution is gently humped, with P~0.2 at the ends (but, that's with 0.1 step size; actually it must ->0 at the ends as a continuous function) and a max ~ 0.75 around t=0.5. or 2) product the column data (LibreOffice requires typing all cells for that, so you won't want to do it much!). Tests with just the first 4 callers showed a "hit" about 1/2 the trials, but with the first 10 callers, NO HITS in 11 trials. So I think that scales as the exponent(in #people) of P(bulk _not_on_the_call), which is astronomically small in your problem -- at best, ~0.75^330,000,000 or whatever. Do it by logs! And 2 people, would be the same, because the problem did specify that everyone else was on the call!! --Cheers, this was a fun problem to work on, --Mr. d.02/09/22