  In many real life situations one has $m$ types of random events happening in
chronological order within a time interval and one wishes to predict various
milestones about these events or their subsets. An example is birdwatching.
Suppose we can observe up to $m$ different types of birds during a season. At
any moment a bird of type $i$ is observed with some probability. There are many
natural questions a birdwatcher may have: how many observations should one
expect to perform before recording all types of birds? Is there a time interval
where the researcher is most likely to observe all species? Or, what is the
likelihood that several species of birds will be observed at overlapping time
intervals? Our paper answers these questions using a new model based on random
interval graphs. This model is a natural follow up to the famous coupon
collector's problem.
