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A suitable rare-event limit links these discrete stories to Poisson counts and exponential waiting times.
Conditions: The context is a rare-event limit.; The variables represent counts and waiting times.
A suitable rare-event limit links these discrete stories to Poisson counts and exponential waiting times.
Conditions: The context is a rare-event limit.; The variables represent counts and waiting times.
Counting successes in a fixed block of trials gives a binomial variable, while counting failures before a fixed number of successes gives a negative binomial variable.
Conditions: Trials are independent with a fixed success probability.; The first scenario involves a fixed total number of trials.; The second scenario involves waiting for a fixed number of successes.
Counting successes in a fixed block of trials gives a binomial variable, while counting failures before a fixed number of successes gives a negative binomial variable.
Conditions: Trials are independent with a fixed success probability.; The first scenario involves a fixed total number of trials.; The second scenario involves waiting for a fixed number of successes.