The length of time ,in minutes, for an airplane to obtain clearance for take off at a certainairport is a random variable Y=3X-2,

Tobias Ali

Tobias Ali

Answered question

2021-01-02

The amount of time, in minutes, for an airplane to obtain clearance for take off at a certain airport is a random variable Y=3X-2, where X has the density function
f(x)={14ex4,x>00,else where 
Find the mean and variance of the random variable Y?

Answer & Explanation

unessodopunsep

unessodopunsep

Skilled2021-01-03Added 105 answers

Given mean of random variable X is E(X)=1λ=4 since here λ=14 also Y=3X2
Therefore mean of random variable Y
=E(Y)=E(3X2)
=3E(X)2
=3(4)2
=10
variance of the exponential distribution =V(X)=1λ
=16
Therefore variance of Y=V(Y)=V(3X2)
=32var(X)+2
=9(16)+2
=λ

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