Question

State highway M131 connects Harbor Springs, MI with Cross Village, MI (where the Polish restaurant Legs Inn is located). It is very scenic, also known as the “Tunnel of Trees”, but it is also a very narrow road with no passing lanes. It is well worth a drive, but not the kind of road to take if you are in a hurry. On any given day, you are 65% likely to get stuck behind a logging truck that slows you down. If that happens, then on average you pass only 3 bicyclists per hour. Otherwise you are going a bit faster and on average you pass 5 bicyclists per hour. If in either case the number of bicyclists you pass in an hour is Poisson distributed, find the expected value and variance of the number of bicyclists you pass in an hour on any given day driving on the “Tunnel of Trees.”

          State highway M131 connects Harbor Springs, MI with Cross Village, MI (where the Polish restaurant
Legs Inn is located). It is very scenic, also known as the “Tunnel of Trees”, but it is also a very narrow
road with no passing lanes. It is well worth a drive, but not the kind of road to take if you are in a
hurry. On any given day, you are 65% likely to get stuck behind a logging truck that slows you down.
If that happens, then on average you pass only 3 bicyclists per hour. Otherwise you are going a bit
faster and on average you pass 5 bicyclists per hour. If in either case the number of bicyclists you pass
in an hour is Poisson distributed, find the expected value and variance of the number of bicyclists you
pass in an hour on any given day driving on the “Tunnel of Trees.”

Added by Vincent S.

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