Suppose that when an airplane waits on the runway the compan

Suppose that, when an airplane waits on the runway, the company must pay each customer a fee if the waiting time exceeds 3 hours. Suppose that an airplane waits an exponential amount of time on the runway, with average 1.5 hours. If the waiting time X, in hours, is bigger than 3, then the company pays each customer 100(X - 3) dollars (otherwise, the company pays nothing). What is the amount that the company expects to pay for a customer on the airplane?

Solution

fX(x)=bexp{-bx}, b=1/1.5

amount company has to pay to customer if plane is late than 3 hours is

=\\int{3}{\\infinity}fX(x)*(x-3)*100dx

=\\int{3}{\\infinity}bexp{-bx}(x-3)*100dx=(100/b)*exp{-3b}= 20.3 $

so company expects to pay for a customer on the airplane will be 20.3 $