Simple sample variance problem

  1. The length of time, in minutes, for an airplane to obtain clearance for takeoff is a random variable Y = 4X + 2, where X has the density function:

    f(x) = 1/3 e^(-x/3) for x > 0

    Find the variance of Y.


    I found the expected value of X to be 14 minutes, which was correct. This means the variance for X will be: E(X^2) - E(X) = 18 - 14 = 4. Will the following work for the variance?

    Var(Y) = (4^2)(4) = 64.

    If so, what does that mean to have a "negative" take off time?

    Thanks for your help!! :)
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,315
    Staff Emeritus
    Science Advisor

    The variance is NOT "E(X^2)- E(x)" it is E(X^2)- (E(x))^2.
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