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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.
The geometric distribution describes the number of failures before the first success, provided the trials are independent and the success probability remains fixed.
Conditions: Trials are independent.; Success probability is fixed.; The convention counts the number of failures before the first success.
The geometric distribution describes the number of failures before the first success, provided the trials are independent and the success probability remains fixed.
Conditions: Trials are independent.; Success probability is fixed.; The convention counts the number of failures before the first success.
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.