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Homework Help: Help with integration please

  1. Nov 9, 2007 #1
    1. The problem statement, all variables and given/known data

    The random variable X has a double-exponential distribution with parameter p>0 if its density is given by

    f_x (x) = (1/2)e^(-p|x|) for all x.

    Show that the expected value of X = 0.

    2. Relevant equations

    I know that the expected value of a random variable x is

    ∫ x * f(x) dx

    3. The attempt at a solution

    We are told that f_x (x) = (1/2)e^(-p|x|)

    So I'm guessing you have to do the following integral going from 0 to infinity:

    ∫ x * (1/2)e^(-p|x|) dx

    But I'm unsure about how to compute this integral.
    Last edited: Nov 9, 2007
  2. jcsd
  3. Nov 9, 2007 #2


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    Science Advisor
    Homework Helper

    If your sample space is [itex][0,\infty)[/itex], how could the average value of X be 0?
    Also, there wouldn't be a need for absolute values if x couldn't be negative.
    I`m sure that the problem implicitly assumes that X can take all values in R.

    You could evaluate the integral by splitting it in two pieces.
    There's a faster way though. Maybe drawing the graph of f will help.
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