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Math Help - Variance from MGF

  1. #1
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    Variance from MGF

    Could you please help me with the following, I know you have to differentiate but I am not saure if I am doing it right, could you please show intermediate steps.

    If X has the moment generating function given by

    MX(t) = cos(7.21t)+ 7.21t* sin(24.85t)

    what is the variance of X ?



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  2. #2
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    Quote Originally Posted by javs156 View Post
    Could you please help me with the following, I know you have to differentiate but I am not saure if I am doing it right, could you please show intermediate steps.

    If X has the moment generating function given by

    MX(t) = cos(7.21t)+ 7.21t* sin(24.85t)

    what is the variance of X ?


    You should know that:

    M_X'(0) = E(X).

    M_X''(0) = E(X^2).

    Therefore Var(X) = E(X^2) - [E(X)]^2 = M_X''(0) - [ M_X'(0) ]^2.

    If you show your working it will be much easier to check if you're "doing it right".
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