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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