Results 1 to 2 of 2

Math Help - Multiplying independent random variables

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    182
    Thanks
    1

    Multiplying independent random variables

    If iv got independent random variables Y1 ~ LN(1, v^2) and Y2 ~ LN(2, 2 v^2)....

    am i right in thinking that X=Y1+Y2 has distribution LN(3, 3 v^2)?

    How do i find the distribution of W=Y1Y2?
    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 sirellwood View Post
    If iv got independent random variables Y1 ~ LN(1, v^2) and Y2 ~ LN(2, 2 v^2)....

    am i right in thinking that X=Y1+Y2 has distribution LN(3, 3 v^2)?

    How do i find the distribution of W=Y1Y2?
    Theorem: If X and Y are two independent and continuous random variables with pdf’s f(x) and g(y) respectively, then the sum U = X + Y is a continuous random variable with pdf given by \displaystyle h(u) = \int_{-\infty}^{+\infty} f(u - y) \, g(y) \, dy.


    Theorem: If X and Y are two independent and continuous random variables with pdf’s f(x) and g(y) respectively and Pr(X = 0) = Pr(Y = 0) = 0, then the product U = XY is a continuous random variable with pdf given by \displaystyle h(u) = \int_{-\infty}^{+\infty} \frac{1}{|y|} \, f \left(\frac{u}{y}\right) \, g(y) \, dy.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sup of independent random variables
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 23rd 2010, 02:34 PM
  2. independent random variables
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 15th 2009, 02:55 PM
  3. X,Y Random Variables, X+Y , 1 are independent?
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: October 1st 2009, 03:32 PM
  4. independent random variables
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: January 26th 2009, 07:37 PM
  5. Independent Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: January 17th 2009, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum