Results 1 to 2 of 2

Math Help - How to determine pdf region

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    4

    How to determine pdf region

    Hi,

    I have difficulty to understand the regions of integration for pdf, so here is some examples, I would appreciate if you can help:

    So lets say we have  f(y_1, y_2) , and we want to show that it is a valid pfd so:

     \int\int f(y_1,y_2) ~dy_1 ~dy_2 = 1 Now:

    Example 1:  <br />
0 <= y_1 <= 2, 0<= y_2 <= 1, 2y_2 < y_1


     \int_{0}^{2}\int_{0}^{y_1/2}    f(x) ~dy_2 ~dy_1<br /> <br />


    Example 2:

     y_1 -1  <= y_2 <= 1-y_1 , 0 <= y_1 <= 1

     \int_{0}^{1}\int_{y_1 - 1}^{1-y_1} f(x) ~dy_2 ~dy_1

    Example 3:

     0 <= y_1 <= y_2, y_1 + y_2 <= 2

    I don't have any idea here

    thanks for the help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2009
    Posts
    105
    Quote Originally Posted by hitman View Post
    Hi,

    I have difficulty to understand the regions of integration for pdf, so here is some examples, I would appreciate if you can help:

    So lets say we have  f(y_1, y_2) , and we want to show that it is a valid pfd so:

     \int\int f(y_1,y_2) ~dy_1 ~dy_2 = 1 Now:

    Example 1:  <br />
0 <= y_1 <= 2, 0<= y_2 <= 1, 2y_2 < y_1


     \int_{0}^{2}\int_{0}^{y_1/2} f(x) ~dy_2 ~dy_1<br /> <br />


    Example 2:

     y_1 -1 <= y_2 <= 1-y_1 , 0 <= y_1 <= 1

     \int_{0}^{1}\int_{y_1 - 1}^{1-y_1} f(x) ~dy_2 ~dy_1

    Example 3:

     0 <= y_1 <= y_2, y_1 + y_2 <= 2

    I don't have any idea here

    thanks for the help
    It would help if you posted the complete and unexpurgated version of eg. 3 that is in the book that you got it from.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. determine a region in the xy plane...
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: January 25th 2011, 11:02 PM
  2. determine the region where product <0
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: September 2nd 2010, 01:42 AM
  3. Replies: 1
    Last Post: May 18th 2010, 11:31 PM
  4. Replies: 1
    Last Post: April 22nd 2009, 04:05 AM
  5. region
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 23rd 2008, 07:16 PM

Search Tags


/mathhelpforum @mathhelpforum