has the density function
f(x)
=
Ste-1,
1⁄e-², x>0
е
otherwise
(a) Airport X is awarded as an 'excellent' airport. An 'excellent' airport would certainly
consider if it is likely to obtain clearance for takeoff within 15 minutes. Comment on
this by determining P(X < 15).
[8 marks]
(b) What is the probability that the airplane obtains clearance for takeoff in the first 5
[6 marks]
minutes?
Find the mean and variance of Y.
(c) The length of time for an airplane to obtain clearance for takeoff at Airport Y is a
random variable
Y = 4X - 3.
[16 marks]
[Q3 Total: 30 marks]
Fig: 1