Results 1 to 3 of 3

Math Help - Marginal variance with two random variables

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    79

    Marginal variance with two random variables

    If ten fair six-sided dice are rolled, suppose that X is the total number of even numbers shown and Y is the total number of fives shown.
    (a) What is the joint p.m.f. of X and Y ?
    (b) What is the marginal variance of X? Can you answer this question in one line, using an argument that does not involve any summation?


    I found for (a) that f(x,y) = ((1/2)^x)*((1/6)^y)*((1/3)^(10-x-y))*10!/(x!y!(10-x-y)!).
    But I really don't know how to approach (b). How can you tell the marginal variance of X without doing all of the summations?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by uberbandgeek6 View Post
    If ten fair six-sided dice are rolled, suppose that X is the total number of even numbers shown and Y is the total number of fives shown.
    (a) What is the joint p.m.f. of X and Y ?
    (b) What is the marginal variance of X? Can you answer this question in one line, using an argument that does not involve any summation?


    I found for (a) that f(x,y) = ((1/2)^x)*((1/6)^y)*((1/3)^(10-x-y))*10!/(x!y!(10-x-y)!).
    But I really don't know how to approach (b). How can you tell the marginal variance of X without doing all of the summations?
    I think I would write the joint distribution as:

    f_{XY}(x,y)=p(y|x)p(x)=b(y,(10-x),1/3)b(x,10,1/2)

    or at least said that this is a multinomial distribution (they expand to the same thing and apperars to be what you have above).




    CB
    Last edited by CaptainBlack; October 20th 2010 at 12:31 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by uberbandgeek6 View Post
    If ten fair six-sided dice are rolled, suppose that X is the total number of even numbers shown and Y is the total number of fives shown.
    (a) What is the joint p.m.f. of X and Y ?
    (b) What is the marginal variance of X? Can you answer this question in one line, using an argument that does not involve any summation?

    It will take more than a line to explain it, but it is faily ellementary:

    var(x)=\sum_x\sum_y (x-\overline{x})^2 p(y|x)p(x)=\sum_x (x-\overline{x})^2 p(x)=10(1/2)^2

    or if you like the marginal variance must be the variance of the binomial distribution of $$ X without any reference to $$ Y.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Marginal pdf of 2 dimensional random variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 20th 2011, 09:47 AM
  2. Variance, Means and Random Variables.
    Posted in the Statistics Forum
    Replies: 2
    Last Post: January 31st 2011, 10:58 AM
  3. What is the variance of the division of 2 random variables?
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: March 23rd 2010, 12:23 PM
  4. Covariance/variance with two random variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 2nd 2009, 01:12 PM
  5. random variables and variance
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 26th 2008, 01:25 AM

Search Tags


/mathhelpforum @mathhelpforum