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Distribution Function f(x)= .5e^|x|, find EX and Var(x)

  1. Nov 5, 2009 #1
    Let X be a continuous random variable with density function

    f(x)= .5e^|x|

    for x range R. Find EX and Var(x)

    help please!
     
  2. jcsd
  3. Nov 5, 2009 #2

    HallsofIvy

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    Check your problem again. That is NOT a density function. [itex]\int_{-\infty}^\infty f(x)dx[/itex] is not even defined, much less being 1. Did you mean [itex]f(x)= 0.5e^{-|x|}[/itex]?
     
  4. Nov 5, 2009 #3
    haha yeah its f(x)= 0.5e^{-|x|}

    sorry about that.
     
  5. Nov 6, 2009 #4

    HallsofIvy

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    Then [itex]E(x)= \int_{-\infty}^{\infty}xe^{-|x|}dx[/itex] which you should be able to get by "symmetry" without needing to do the integral.

    And then [itex]Var(X)= \int_{-\infty}^{\infty}x^2e^{-|x|}dx= 2\int_0^\infty x^2e^{x}dx[/itex] which you can do integrating by parts (twice).
     
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