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Characteristic function of z (Joint?)

  1. Jan 21, 2012 #1
    I need some help. Is there a good way to do this type of question?

    1. The problem statement, all variables and given/known data
    Let X and Y be independent random Variables with exponential densities

    fX(x) = Ωe-Ωx, if X≥0
    0, otherwise

    fY(y) = βe-βy, if y≥0
    0, otherwise



    Respectively, where η and β are positive real-valued constants.

    1) Find the characteristic function ∅z of Z = X+Y
    2) Find the probability density function fZ(z) of Z = X+Y

    2. Relevant equations

    N/A
     
    Last edited: Jan 21, 2012
  2. jcsd
  3. Jan 21, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Yes, a good way to do this type of question is to use the results in your course notes and/or textbook, and to just go ahead and use the formulas. If you show your work and if you get stuck on some specific point, then come back and ask for advice.

    RGV
     
  4. Jan 21, 2012 #3
    Well, by textbook ( or teachers .pdf ) does not explain how to do this kind of problem. I also found it difficult to find something about in on the internett that i understood.(Yes math is not one of my strongest subjects).

    How should i begin to solve this problem?
     
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