Moment generating function

  • Thread starter Tomp
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  • #1
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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
 

Answers and Replies

  • #2
statdad
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I would prefer to see the second form.
 
  • #3
HallsofIvy
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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"!)
 
  • #4
statdad
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Typesetting preferences :)

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"!)
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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