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Conditional moment generating functions

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data
    Random variable U is continuous uniform in the time interval (0,2)
    T|U (T given U) is modelled by the mgf [tex]\frac{1}{1-ut}[/tex]
    Find:
    a) E(U)
    b) E(T|U) and Var(T|U)
    c) E(T) and Var(T)


    2. Relevant equations



    3. The attempt at a solution
    a) This one was fine, E(U)=1
    b) I know E(X)=m'(0), but how does it work with conditional distributions?
    c) Again, not sure how I find the marginal distribution of T from the conditional mgf.

    Any pointers appreciated. :)
     
  2. jcsd
  3. Sep 17, 2010 #2

    statdad

    User Avatar
    Homework Helper

    How do you use any mgf to find the mean of the underlying variable? The same method applied to

    [tex]
    \frac 1 {1-ut}
    [/tex]

    will give E(T | U) (it will be a function of U), and you can also use the conditional mgf to find V(T | U) (another function of U). To find the unconditional expectation and Variance of T, use the notion of double expectation. (E(T) = E(E(T|U)))
     
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