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Math Help - Question:Means and variances of linear combinations of random variables

  1. #1
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    Question:Means and variances of linear combinations of random variables

    The length of time, in minutes, for and 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) = { 1/4e^(-x/4), x>0
    0, elsewhere,

    Find the mean and variance of the random variable Y.

    the answer from the text book are: mean of Y = 10, variance = 144;

    anyone know how to get the answers?
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    \begin{array}{l}<br />
 E(Y) = \int\limits_0^\infty  {Yf(x)dx}  = \int\limits_0^\infty  {\left( {3x - 2} \right)f(x)dx}  \\ <br />
 E(Y^2 ) = \int\limits_0^\infty  {Y^2 f(x)dx}  = \int\limits_0^\infty  {\left( {3x - 2} \right)^2 f(x)dx}  \\ <br />
 V(Y) = E(Y^2 ) - E^2 (Y) \\ <br />
 \end{array}
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