Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By chiro

Math Help - I have a question regarding the normal distribution!!

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    London
    Posts
    2

    I have a question regarding the normal distribution!!

    Hi,
    I have a question reagrding the normal distribution.
    Suppose there are 3 normal distribution equations as follows

    X1~N(5,9)
    X2~N(10,16)
    X3~N(5+10,9+16)

    And I used Excel to generate random numbers for different normal distributions.
    Then I found that the sum of X1+X2 equals X3.
    Can anyone please explain me why X1+X2 equals X3?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: I have a question regarding the normal distribution!!

    Hey theconman12345.

    You can use the moment generating function of the sum of two independent normal distributions is a normal and you can use the fact that E[X+Y] = E[X] + E[Y] and Var[X+Y] = Var[X] + Var[Y] to show you get the mean and variance added when they are independent.

    The MGF proof is obtained by considering that if X and Y are independent, then E[e^(t{X+Y})] = E[e^tX]E[e^tY] = MGF_x(t)*MGF_y(t) and you can take it from there.
    Thanks from theconman12345
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    London
    Posts
    2

    Re: I have a question regarding the normal distribution!!

    thank you for your help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Normal Distribution Question.
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 26th 2012, 04:36 PM
  2. Question on normal distribution #2
    Posted in the Statistics Forum
    Replies: 9
    Last Post: September 16th 2010, 05:07 AM
  3. Question on Normal Distribution
    Posted in the Statistics Forum
    Replies: 3
    Last Post: May 9th 2010, 05:28 PM
  4. Normal distribution question.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 23rd 2009, 06:52 PM
  5. normal distribution question
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: September 10th 2009, 03:22 AM

Search Tags


/mathhelpforum @mathhelpforum