probability theory question: mean subsequent block time (monero.town)

submitted 2 weeks ago* (last edited 2 weeks ago) by chaser@monero.town to c/monero@monero.town

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I'm trying to arrive at the function that describes the following, but can't quite figure it out for multiple blocks. (there are some useful insights for a single block here.)

assume the Poisson point process that is the arrival of proof-of-work blocks on Monero. the mean of the block times is the target block time t (120 seconds).

also assume n subsequent blocks.

also assume p, the probability of n subsequent blocks having a mean block time less than or equal to T.

given t, n and p, how can I calculate T?

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[-] chaser@monero.town 1 points 1 week ago

thank you very much, Rucknium. your understanding of my question was spot-on, and the R code works excellently! very useful.

I'd like to ask a few more questions:

is 314 a common seed in R, or just something you randomly picked?
in statistics in general, are there cases where n * 100000 random samples (any distribution) would be insufficient? is it a good rule of thumb?