Results 1 to 3 of 3

Math Help - Moment Generating function of a normal variable

  1. #1
    Junior Member
    Joined
    Nov 2011
    Posts
    27

    Moment Generating function of a normal variable

    Hi everybody,

    Again a problem with deriving an MGF.

    I don't understand the manipulation in the first row. Why is e^xt disappearing? Why do we choose to make this (yellow marked) specific substitution.... = + σ^2*t.


    Thanks for your help!
    [IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
    [IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
    [IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
    Attached Thumbnails Attached Thumbnails Moment Generating function of a normal variable-mgf-normal-variable.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Moment Generating function of a normal variable

    Quote Originally Posted by Marmy View Post
    Hi everybody,

    Again a problem with deriving an MGF.

    I don't understand the manipulation in the first row. Why is e^xt disappearing? Why do we choose to make this (yellow marked) specific substitution.... = + σ^2*t.


    Thanks for your help! [IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
    [IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
    [IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
    The e^(xt) has not disappeared. Expand the exponent in the second integral and it clearly appears.

    The reason for the substitution is clear from the entire solution ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2011
    Posts
    27

    Re: Moment Generating function of a normal variable

    Thanks,

    I managed to understand this problem now!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Moment Generating function of a gamma variable
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 9th 2012, 01:27 PM
  2. Moment generating function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 24th 2009, 02:47 PM
  3. Moment Generating for Normal
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: August 7th 2009, 04:27 AM
  4. moment generating function
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: May 16th 2009, 04:02 AM
  5. Method of moment generating function normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 25th 2008, 03:22 AM

Search Tags


/mathhelpforum @mathhelpforum