1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]
    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


    User Avatar
    Homework Helper

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

    \frac 1 {1-ut}

    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)))
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook