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Moment generating function

  1. Apr 11, 2013 #1
    Question
    A moment-generating function of X is given by M(t) = 0.3e^t + 0.4e^(2t) + 0.2e^(3t) + 0.1e^(5t)

    Find the pmf of X

    My attempt
    x f(x)
    1 0.3
    2 0.4
    3 0.2
    4 0
    5 0.1

    I am just wondering whether it is correct to say "0" for 4 or is it more correct to say

    x f(x)
    1 0.3
    2 0.4
    3 0.2
    5 0.1

    or is either acceptable
     
  2. jcsd
  3. May 28, 2013 #2

    statdad

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    Homework Helper

    I would prefer to see the second form.
     
  4. May 29, 2013 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I, on the other hand, prefer the first. I think if I were to look at the second I would wonder whether or not the "5" was a typo and "4" was meant. The first form makes it clear.

    (Though my "inner typesetter" would prefer "4 0.0"!)
     
  5. May 31, 2013 #4

    statdad

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    Homework Helper

    Typesetting preferences :)

    Understandable. My thought process was simple: in a small discrete distribution, if some integer value has probability zero, don't bother including it in a summary table.
     
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