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Monero blocks are on average 2 minutes apart, but how much is the variation?
What is the standard deviation of block times generation time?
Can the above question be modeled as an exponential distribution?
What has been the longest period between two blocks so far?
Yes an an exponential distribution can be used but it will require some assumptions:
No propagation delays of block discoveries
Constant difficulty
Accurate time stamps
With those assumptions and an exponential distribution the standard deviation equal to the expected block time (expectancy value) which is currently 120 seconds (2 minute blocks).
Assumptions #1 and #2 above will never be completely true. Monero Research Labs is now researching Difficulty Adjustment Algorithms in Cryptocurrency Protocols and is considering such factors as dishonestly reporting time stamps.
I am not sure about the longest time between blocks, but here is my best guess which occurred about 28 and a half minutes after this block. This was the time period just following the hard fork that moved Monero from 1 minute to 2 minute blocks.
