From events/min to max_events/sec

[thehobbit30]

I have a set of statistically independent events for which I know the count over a timeframe of a minute. Is it possible to determine the max number of events that might have occurred at the same second?

For example, I know that I had 3,000 events at a given minute. The average number of events per second would be 50, but that's not what I am after as there could have been seconds with 5 events and seconds with 90 events. Is it possible to determine the peak number of events/sec throughout that minute? I suppose that the result would be a PDF too, in which case I'd be interested in the most likely outcome.


PS: It's been a couple of decades since I last looked into these sort of problems. I am clearly very rusty, so forgive any nonsense.

 

[HallsofIvy]

Unless you are given some other information, it is possible that all 3000 events happened in the first second and no events after. Or it is possible that exactly 50 events occurred every second. In the first case, the maximum number of events per second is 3000 and in the second case, it is 50. And, of course, any number between the two is possible. In order to determine a "PDF" or most likely outcome, you would have to be given a PDF for the individual events.