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Math Help - [SOLVED] Moment Generating Function

  1. #1
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    [SOLVED] Moment Generating Function

    Consider a discrete random variable X with the probability mass function as:
    x 2 4 6 8 10 16
    P(x) 0.1 0.2 0.35 0.2 0.1 0.05


    Find the moment generating function of X.


    Do I set it up as this?
    0.1e^2t + 0.2e^4t + 0.35e^6t + 0.2e^8t + 0.1e^10t + 0.05e^16t
    If so, what do I do from there? I feel like I'm on the total wrong track here.
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  2. #2
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    Quote Originally Posted by ban26ana View Post
    Consider a discrete random variable X with the probability mass function as:
    x 2 4 6 8 10 16
    P(x) 0.1 0.2 0.35 0.2 0.1 0.05


    Find the moment generating function of X.


    Do I set it up as this?
    0.1e^2t + 0.2e^4t + 0.35e^6t + 0.2e^8t + 0.1e^10t + 0.05e^16t
    If so, what do I do from there? I feel like I'm on the total wrong track here.
    Yes. Your answer is correct.

    You could simplify by taking out a common factor of 0.05 e^{2t} but I don't see why you'd bother.
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  3. #3
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    So that's the final answer? For the rest of the problems, I got t<-ln(?), where the ? was a number like 0.1. Is my final answer for this the long equation that I typed? I just confused myself.
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  4. #4
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    Quote Originally Posted by ban26ana View Post
    So that's the final answer? For the rest of the problems, I got t<-ln(?), where the ? was a number like 0.1. Is my final answer for this the long equation that I typed? I just confused myself.
    I said your answer was correct, didn't I? As for the rest of the problems, I can't comment on what I can't see.
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    I said your answer was correct, didn't I? As for the rest of the problems, I can't comment on what I can't see.
    Thanks. I guess it just didn't look right to me. But then, if I knew what I was doing, I wouldn't be on here asking questions.
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