Results 1 to 11 of 11

Math Help - Moment Generating Function

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    20

    Moment Generating Function

    Can someone explain to me how this problem works?

    Given the moment generating function Mx(t)=e^(3t+8t^2), find the moment generating function of the random variable Z=1/4(X-3) and use it to determine the mean and the variance of Z.

    I don't understand why its asking you to find another mgf if one is given to you already. Thanks!
    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
    Quote Originally Posted by xuyuan View Post
    Can someone explain to me how this problem works?

    Given the moment generating function Mx(t)=e^(3t+8t^2), find the moment generating function of the random variable Z=1/4(X-3) and use it to determine the mean and the variance of Z.

    I don't understand why its asking you to find another mgf if one is given to you already. Thanks!
    See 6.7 here: http://www.am.qub.ac.uk/users/g.gribakin/sor/Chap6.pdf
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Mx(t)=e^(3t+8t^2) is the MGF of X

    you are asked to get the MGF of Z=X/4-3/4 if I understand your ().
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2009
    Posts
    20
    Quote Originally Posted by matheagle View Post
    Mx(t)=e^(3t+8t^2) is the MGF of X

    you are asked to get the MGF of Z=X/4-3/4 if I understand your ().
    Hm, so I read through what was posted and my textbook, but I still don't quite understand. So I have the MGF of X, then to get the MGF of Z do I need to integrate Z from negative to positive infinity and somehow subsitute in X? This is really confusing me, any help is appreciated thanks!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Just substitute, or recognize the distribution of X and use that.

    Z=X/4-3/4

    So M_Z(t)=E(e^{Zt})=E(e^{(X/4-3/4)t})=e^{(-3/4)t}E(e^{Xt/4})

    =e^{(-3/4)t}E(e^{X(t/4)})=e^{(-3/4)t}M_X(t/4)

    Plug in t/4 for t in the mgf of X and examine what you have.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by xuyuan View Post
    Hm, so I read through what was posted and my textbook, but I still don't quite understand. So I have the MGF of X, then to get the MGF of Z do I need to integrate Z from negative to positive infinity and somehow subsitute in X? This is really confusing me, any help is appreciated thanks!
    You're probably expected to know and apply the result found at the bottom of page 1 here: http://web.as.uky.edu/statistics/use...320u04/mgf.pdf

    In fact, it's the same result that I refered you to in my first reply. Did you in fact bother to click on the link and look at it?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2009
    Posts
    2
    Hi, I've been working on the same problem and came to the answer
    Mz(t)=e^[(4/5)t^2]

    Is this the answer that you came to?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by nnnikii View Post
    Hi, I've been working on the same problem and came to the answer
    Mz(t)=e^[(4/5)t^2]

    Is this the answer that you came to?
    I get a different answer. Please pm me your working.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Nov 2009
    Posts
    2
    Oopsie!! I just went over my calculation and realized I made a mistake. My new answer is

    Mz(t)=e^[(1/2)t^2]

    Is that correct?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by nnnikii View Post
    Oopsie!! I just went over my calculation and realized I made a mistake. My new answer is

    Mz(t)=e^[(1/2)t^2]

    Is that correct?
    Yes.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    The point of this problem is that a linear transformation of a normal is a normal.
    The mean and variance should be easy to calculate directly.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Moment Generating function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 25th 2011, 01:49 PM
  2. Moment-Generating Function - Need help!!!
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 1st 2009, 05:40 PM
  3. moment-generating function
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: May 3rd 2008, 07:34 PM
  4. Moment-generating Function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 28th 2008, 06:41 AM
  5. Moment generating function
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: February 2nd 2008, 01:27 AM

Search Tags


/mathhelpforum @mathhelpforum