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Math Help - Moment Generating Function

  1. #1
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    Moment Generating Function

    I have a problem that gives me a M.G.F and asks for P(1< or = X < or = 2)

    For example M(t)= (0.3 + 0.7 e^t)^5

    P(1< or = X < or = 2) = 0.1607

    How is that done? I can't find the principle in my text.
    I know that P(2) is equal to M(2) but how about the above example ?


    Edit: If possible please post a link to a a page that explain how to use M.G.F , I'm having problems with various applications. Like how to get the M.G.F from E(X).
    Last edited by Hitman6267; July 10th 2010 at 12:24 PM.
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  2. #2
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    Quote Originally Posted by Hitman6267 View Post
    I have a problem that gives me a M.G.F and asks for P(1< or = X < or = 2)

    For example M(t)= (0.3 + 0.7 e^t)^5

    P(1< or = X < or = 2) = 0.1607

    How is that done? I can't find the principle in my text.
    I know that P(2) is equal to M(2) but how about the above example ?


    Edit: If possible please post a link to a a page that explain how to use M.G.F , I'm having problems with various applications. Like how to get the M.G.F from E(X).
    You're meant to recognise this as the mgf of a random variable that follows a binomial distribution. Your job is to get from it the values of n and p, and then to use the now known mass density function to calculate the required probability.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    You're meant to recognise this as the mgf of a random variable that follows a binomial distribution. Your job is to get from it the values of n and p
    I was able to do that.
    n=5
    p=0.7


    But what does P(1< or = X < or = 2) mean ? The probability of what ?
    Also unless I'm mistaken we haven't learned the mass density function.
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  4. #4
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    Quote Originally Posted by Hitman6267 View Post
    I was able to do that.
    n=5
    p=0.7


    But what does P(1< or = X < or = 2) mean ? The probability of what ?
    Also unless I'm mistaken we haven't learned the mass density function.
    Well, I have no idea what P(1< or = X < or = 2) means. It would help if you typeset your equation properly using latex. From what I can understand, P(1< or = X < or = 2) might mean \Pr(1 \leq X = 2), which would give an answer of zero because you cannot be equal to 2 and less than or equal to 1. But I doubt that's what the original question intends.

    By the way, are you saying that you know nothing given here: Binomial distribution - Wikipedia, the free encyclopedia
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    It's P(1 \leq X \leq 2)

    I've been taught everything in that wikipedia page except the covariance.
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  6. #6
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    Quote Originally Posted by Hitman6267 View Post
    It's P(1 \leq X \leq 2)

    I've been taught everything in that wikipedia page except the covariance.
    Then you have to calculate Pr(X = 1) + Pr(X = 2). And you do that using the pmf for a binomial variate with parameters n = 5 and p = 0.7.
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