Question

The length of time, in minutes, for an airplaneto obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the densityfunction f(x)=\left\{\begin{array}{ll}

\frac{1}{4} e^{-x / 4}, & x>0 \\

0, & \text { elsewhere. }

\end{array}\right. Find the mean and variance of the random variable Y.

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