Is My Probability Mass Function Correct Given the MGF?

[Tomp]

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

 

[statdad]

I would prefer to see the second form.

 

[HallsofIvy]

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"!)

 

[statdad]

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.

 

[blue_raver22]

?Both options are acceptable, as long as the probabilities add up to 1. The moment-generating function does not provide information on the probability of the value 4, so either option is valid. However, in order to be consistent with the given moment-generating function, it may be more appropriate to assign a probability of 0 to the value 4.