For an interarrival distribution F having mean , we defined the equilibrium distribution of F, denoted Fe,

For an interarrival distribution F having mean μ, we defined the equilibrium distribution of F, denoted Fe, by

(a) Show that if F is an exponential distribution, then F = Fe.

(b) If for some constant c,

show that Fe is the uniform distribution on (0, c). That is, if interarrival times are identically equal to

c, then the equilibrium distribution is the uniform distribution on the interval (0, c).

(c) The city of Berkeley, California, allows for two hours parking at all nonmetered locations within one mile of the University of California. Parking officials regularly tour around, passing the same point every two hours.
When an official encounters a car he or she marks it with chalk. If the same car is there on the official’s return two hours later, then a parking ticket is written. If you park your car in Berkeley and return after three hours, what is the probability you will have received a ticket?

Transcribed Image Text:

Fe(x): 1 x fu Jo [1 - F(y)]dy