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Is it possible for the following to happen:

Some moment of a distribution does not exist. Then can the mgf exist for any t not equal to zero?

user3236841
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    See some examples [here](http://stats.stackexchange.com/a/32787/2970). But, in general, think about the case where $X$ is nonnegative almost surely with an *arbitrary* distribution and $t < 0$ (**Hint**: Monotonicity.). – cardinal Feb 12 '17 at 19:50
  • I am sorry: I do not quite understand the answer. Thanks for the link. The question is if a moment does not exist, can the mgf exist for some non-zero t? The link does not cover this case, or does it? I am sorry again and thank you for your help. – user3236841 Feb 12 '17 at 20:08
  • I realize the comment by @Cardinal is cryptic, but doesn't the paragraph following "What does the mgf say about the moments?" in his reference fully address your question? – whuber Feb 12 '17 at 20:58
  • Thanks, got it! The proposition there proves it. THanks again to all!! – user3236841 Feb 12 '17 at 22:33

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